Edit Profile (opens in new tab) Holm, Darryl D. Compute Distance To: Compute Author ID: holm.darryl-d Published as: Holm, Darryl D.; Holm, D. D.; Holm, Darryl Homepage: http://wwwf.imperial.ac.uk/~dholm/ External Links: MGP · ORCID · Wikidata · ResearchGate · Math-Net.Ru · dblp · GND · IdRef Documents Indexed: 231 Publications since 1978, including 7 Books 6 Contributions as Editor · 1 Further Contribution Co-Authors: 133 Co-Authors with 199 Joint Publications 3,604 Co-Co-Authors all top 5 Co-Authors 38 single-authored 20 Ratiu, Tudor Stefan 15 Cotter, Colin John 15 Gay-Balmaz, François 15 Marsden, Jerrold Eldon 15 Putkaradze, Vakhtang 14 Tronci, Cesare 11 Gibbon, John D. 11 Kupershmidt, Boris A. 10 Camassa, Roberto 10 Ivanov, Rossen I. 7 Arnaudon, Alexis 7 Crisan, Dan O. 7 Titi, Edriss Saleh 5 Alber, Mark S. 5 Chen, Shiyi 5 Foiaş, Ciprian Ilie 5 Geurts, Bernard J. 5 Kovačič, Gregor 5 Meier, David M. 4 Ellis, David C. P. 4 Fabijonas, Bruce R. 4 Mininni, Pablo D. 4 Olson, Eric J. 4 Percival, James R. 4 Pouquet, Annick G. 3 Bruveris, Martins 3 Doering, Charles Rogers 3 Gibbons, John 3 Gottwald, Georg A. 3 Graham, Jonathan Pietarila 3 Jacobs, Henry O. 3 Levermore, C. David 3 Luesink, Erwin 3 Nicolaenko, Basil 3 Pan, Wei 3 Sommer, Stefan 3 Tratnik, M. V. 3 Tyranowski, Tomasz M. 3 Wingate, Beth A. 2 Abarbanel, Henry D. I. 2 Allen, John S. 2 Bender, Carl M. 2 Bethencourt de León, Aythami 2 Cendra, Hernán 2 Cruzeiro, Ana-Bela 2 De Castro, Alex Lucio 2 Drivas, Theodore Dimitrios 2 Dullin, Holger R. 2 Fedorov, Yuri N. 2 Hecht, Matthew W. 2 Hone, Andrew N. W. 2 Hook, Daniel W. 2 Hyman, James M. 2 Kerr, Robert M. 2 Margolin, Len G. 2 Pelloni, Beatrice 2 Petersen, Mark R. 2 Staley, Martin F. 2 Stechmann, Samuel N. 2 Takao, So 2 Vialard, François-Xavier 2 Weinstein, Alan David 2 Wynne, Shannon 1 Aceves, Alejandro B. 1 Albeverio, Sergio A. 1 Almaguer, Juan Antonio 1 Alonso-Orán, Diego 1 Axford, Roy A. 1 Bayly, Bruce J. 1 Bechtel, Stephen E. 1 Benoit, Sylvain 1 Berman, Gennady P. 1 Bishop, Alan Reginald 1 Bröcker, Jochen 1 Brody, Dorje C. 1 Bulgakov, Evgeny N. 1 Burnett, Christopher L. 1 Calderhead, Ben 1 Cao, Chongsheng 1 Castrillón López, Marco 1 Chang, Dong Eui 1 Chen, Qiaoning 1 Cheraghi, Davoud 1 Cheskidov, Alexey 1 Degasperis, Antonio 1 Doolen, Gary D. 1 Duan, Jinqiao 1 Ecke, Robert E. 1 Eldering, Jaap 1 Eyink, Gregory L. 1 Flandoli, Franco 1 Forest, Mark Gregory 1 Foskett, Michael S. 1 Fringer, Oliver B. 1 Gabitov, Ildar R. 1 Gjaja, Ivan M. 1 Hameiri, Eliezer 1 Henry, David 1 Herrera, Julio E. 1 Hone, N. W. ...and 40 more Co-Authors all top 5 Serials 26 Physica D 15 Journal of Nonlinear Science 13 Journal of Physics A: Mathematical and Theoretical 9 Nonlinearity 9 Physics of Fluids 9 Physics of Fluids 8 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 7 Journal of Fluid Mechanics 7 Physics Letters. A 7 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 5 Journal of Mathematical Physics 5 Journal of Statistical Physics 5 Journal of Geometric Mechanics 4 Journal of Physics A: Mathematical and General 3 Communications in Mathematical Physics 3 Foundations of Computational Mathematics 2 International Journal of Multiphase Flow 2 Letters in Mathematical Physics 2 Physics Reports 2 Advances in Applied Mathematics 2 Journal of Dynamics and Differential Equations 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Physical Review Letters 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 SIAM Journal on Applied Dynamical Systems 2 Communications in Mathematical Sciences 2 Journal of Geometry and Symmetry in Physics 1 Archive for Rational Mechanics and Analysis 1 Inverse Problems 1 Journal of Computational Physics 1 Journal of Mathematical Analysis and Applications 1 Theoretical and Mathematical Physics 1 Fluid Dynamics Research 1 Journal of Geometry and Physics 1 Advances in Mathematics 1 BIT 1 Indiana University Mathematics Journal 1 Mathematics and Computers in Simulation 1 Philosophical Transactions of the Royal Society of London. Ser. A 1 Quarterly of Applied Mathematics 1 Studies in Applied Mathematics 1 Acta Applicandae Mathematicae 1 Journal of Scientific Computing 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Journal of Mathematical Imaging and Vision 1 Chaos 1 Journal of Nonlinear Mathematical Physics 1 Journal of Turbulence 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Multiscale Modeling & Simulation 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Fields Institute Communications 1 Lectures in Applied Mathematics 1 Lecture Notes in Physics. New Series m: Monographs 1 Oxford Texts in Applied and Engineering Mathematics 1 Discrete and Continuous Dynamical Systems. Series S 1 Kinetic and Related Models 1 Springer Proceedings in Mathematics & Statistics 1 SIAM/ASA Journal on Uncertainty Quantification 1 Proceedings A. Royal Society of London 1 Annals of Mathematical Sciences and Applications 1 Advanced Textbooks in Mathematics all top 5 Fields 136 Fluid mechanics (76-XX) 89 Dynamical systems and ergodic theory (37-XX) 71 Partial differential equations (35-XX) 56 Mechanics of particles and systems (70-XX) 26 Statistical mechanics, structure of matter (82-XX) 22 Probability theory and stochastic processes (60-XX) 22 Geophysics (86-XX) 14 Differential geometry (53-XX) 14 Global analysis, analysis on manifolds (58-XX) 10 Optics, electromagnetic theory (78-XX) 8 General and overarching topics; collections (00-XX) 8 Numerical analysis (65-XX) 8 Mechanics of deformable solids (74-XX) 7 Ordinary differential equations (34-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 5 Topological groups, Lie groups (22-XX) 5 Quantum theory (81-XX) 5 Relativity and gravitational theory (83-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Statistics (62-XX) 3 Biology and other natural sciences (92-XX) 3 Information and communication theory, circuits (94-XX) 2 Computer science (68-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 History and biography (01-XX) 1 Algebraic geometry (14-XX) 1 Nonassociative rings and algebras (17-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 202 Publications have been cited 5,870 times in 3,009 Documents Cited by ▼ Year ▼ An integrable shallow water equation with peaked solitons. Zbl 0972.35521Camassa, Roberto; Holm, Darryl D. 1,410 1993 A new integrable shallow water equation. Zbl 0808.76011Camassa, Roberto; Holm, Darryl D.; Hyman, James M. 369 1994 The Euler-Poincaré equations and semidirect products with applications to continuum theories. Zbl 0951.37020Holm, Darryl D.; Marsden, Jerrold E.; Ratiu, Tudor S. 294 1998 Nonlinear stability of fluid and plasma equilibria. Zbl 0717.76051Holm, D. D.; Marsden, J. E.; Ratiu, T.; Weinstein, A. 227 1985 The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory. Zbl 0995.35051Foias, Ciprian; Holm, Darryl D.; Titi, Edriss S. 184 2002 The Navier-Stokes-alpha model of fluid turbulence. Zbl 1037.76022Foias, Ciprian; Holm, Darryl D.; Titi, Edriss S. 163 2001 On a Leray-\(\alpha\) model of turbulence. Zbl 1145.76386Cheskidov, Alexey; Holm, Darryl D.; Olson, Eric; Titi, Edriss S. 138 2005 Camassa-Holm equations as a closure model for turbulent channel and pipe flow. Zbl 1042.76525Chen, Shiyi; Foias, Ciprian; Holm, Darryl D.; Olson, Eric; Titi, Edriss S. 136 1998 Camassa-Holm, Korteweg-de Vries-5 and other asymptotically equivalent equations for shallow water waves. Zbl 1032.76518Dullin, Holger R.; Gottwald, Georg A.; Holm, Darryl D. 128 2003 Wave structure and nonlinear balances in a family of evolutionary PDEs. Zbl 1088.76531Holm, Darryl D.; Staley, Martin F. 127 2003 A connection between the Camassa-Holm equations and turbulent flows in channels and pipes. Zbl 1147.76357Chen, S.; Foias, C.; Holm, D. D.; Olson, E.; Titi, E. S.; Wynne, S. 106 1999 On asymptotically equivalent shallow water wave equations. Zbl 1050.76008Dullin, H. R.; Gottwald, G. A.; Holm, D. D. 97 2004 Low-dimensional behaviour in the complex Ginzburg-Landau equation. Zbl 0655.58021Doering, Charles R.; Gibbon, John D.; Holm, Darryl D.; Nicolaenko, Basil 95 1988 Nonlinear balance and exchange of stability in dynamics of solitons, peakons, ramps/cliffs and leftons in a 1+1 nonlinear evolutionary PDE. Zbl 1010.35066Holm, Darryl D.; Staley, Martin F. 91 2003 The geometry of peaked solitons and billiard solutions of a class of integrable PDE’s. Zbl 0808.35124Alber, Mark S.; Camassa, Roberto; Holm, Darryl D.; Marsden, Jerrold E. 90 1994 The Camassa-Holm equations and turbulence. Zbl 1194.76069Chen, S.; Foias, C.; Holm, D. D.; Olson, E.; Titi, E. S.; Wynne, S. 88 1999 Geometric mechanics and symmetry. From finite to infinite dimensions. Zbl 1175.70001Holm, Darryl D.; Schmah, Tanya; Stoica, Cristina 73 2009 Variational principles for stochastic fluid dynamics. Zbl 1371.35219Holm, Darryl D. 63 2015 Traveling wave solutions for a class of one-dimensional nonlinear shallow water wave models. Zbl 1062.35080Cao, Chongsheng; Holm, Darryl D.; Titi, Edriss S. 63 2004 Direct numerical simulations of the Navier-Stokes alpha model. Zbl 1194.76080Chen, Shiyi; Holm, Darryl D.; Margolin, Len G.; Zhang, Raoyang 62 1999 Integrable and non-integrable equations with peakons. Zbl 1053.37039Degasperis, A.; Holm, D. D.; Hone, A. N. W. 55 2003 Poisson brackets and clebsch representations for magnetohydrodynamics, multifluid plasmas, and elasticity. Zbl 1194.76285Holm, Darryl D.; Kupershmidt, Boris A. 50 1983 The complex geometry of weak piecewise smooth solutions of integrable nonlinear PDE’s of shallow water and Dym type. Zbl 1001.37062Alber, Mark S.; Camassa, Roberto; Fedorov, Yuri N.; Holm, Darryl D.; Marsden, Jerrold E. 41 2001 Leray and LANs-\(\alpha\) modelling of turbulent mixing. Zbl 1273.76139Geurts, Bernard J.; Holm, Darryl D. 38 2006 Fluctuation effects on 3D Lagrangian mean and Eulerian mean fluid motion. Zbl 1194.76062Holm, Darryl D. 36 1999 Formation of clumps and patches in self-aggregation of finite-size particles. Zbl 1125.82021Holm, Darryl D.; Putkaradze, Vakhtang 35 2006 Regularization modeling for large-eddy simulation. Zbl 1185.76144Geurts, Bernard J.; Holm, Darryl D. 32 2002 Long-time effects of bottom topography in shallow water. Zbl 0899.76081Camassa, Roberto; Holm, Darryl D.; Levermore, C. David 31 1996 Invariant higher-order variational problems. Zbl 1279.58009Gay-Balmaz, François; Holm, Darryl D.; Meier, David M.; Ratiu, Tudor S.; Vialard, François-Xavier 30 2012 Nonlinear stability analysis of stratified fluid equilibria. Zbl 0637.76119Abarbanel, H. D. I.; Holm, D. D.; Marsden, J. E.; Ratiu, T. S. 29 1986 Two-component CH system: inverse scattering, peakons and geometry. Zbl 1216.35175Holm, D. D.; Ivanov, R. I. 29 2011 Multi-component generalizations of the CH equation: geometrical aspects, peakons and numerical examples. Zbl 1213.37097Holm, D. D.; Ivanov, R. I. 28 2010 The Hamiltonian structure of continuum mechanics in material, inverse material, spatial and convective representations. Zbl 0611.70015Holm, D. D.; Marsden, J. E.; Ratiu, T. S. 27 1986 A class of equations with peakon and pulson solutions (with an appendix by Harry Braden and John Byatt-Smith). Zbl 1362.35316Holm, Darryl D.; Hone, N. W. 27 2005 Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics. Zbl 1080.76504Holm, Darryl D. 26 2002 Geometric mechanics. Part I: Dynamics and symmetry. Zbl 1160.70001Holm, Darryl D. 26 2008 Geometric mechanics. Part I: Dynamics and symmetry. 2nd ed. Zbl 1227.70001Holm, Darryl D. 25 2011 Multiple Lie-Poisson structures, reductions, and geometric phases for the Maxwell-Bloch travelling wave equations. Zbl 0884.58042David, D.; Holm, D. D. 25 1992 Symmetry reduced dynamics of charged molecular strands. Zbl 1333.70029Ellis, David C. P.; Gay-Balmaz, François; Holm, Darryl D.; Putkaradze, Vakhtang; Ratiu, Tudor S. 24 2010 Self-consistent Hamiltonian dynamics of wave mean-flow interaction for a rotating stratified incompressible fluid. Zbl 0900.76718Gjaja, Ivan; Holm, Darryl D. 23 1996 The momentum map representation of images. Zbl 1211.58010Bruveris, M.; Gay-Balmaz, F.; Holm, D. D.; Ratiu, T. S. 23 2011 Resonant interactions in rotating homogeneous three-dimensional turbulence. Zbl 1097.76033Chen, Qiaoning; Chen, Shiyi; Eyink, Gregory L.; Holm, Darryl D. 23 2005 Geometric mechanics. Part II: Rotating, translating and rolling. Zbl 1149.70001Holm, Darryl D. 23 2008 Solution properties of a 3D stochastic Euler fluid equation. Zbl 1433.60051Crisan, Dan; Flandoli, Franco; Holm, Darryl D. 22 2019 The Euler-Poincaré theory of metamorphosis. Zbl 1186.68413Holm, Darryl D.; Trouvé, Alain; Younes, Laurent 22 2009 Quaternions and particle dynamics in the Euler fluid equations. Zbl 1145.76012Gibbon, J. D.; Holm, D. D.; Kerr, R. M.; Roulstone, I. 21 2006 Averaged Lagrangians and the mean effects of fluctuations in ideal fluid dynamics. Zbl 1098.76547Holm, Darryl D. 21 2002 On the link between umbilic geodesics and soliton solutions of nonlinear PDEs. Zbl 0835.35125Alber, Mark S.; Camassa, Roberto; Holm, Darryl D.; Marsden, Jerrold E. 21 1995 Hamiltonian chaos in nonlinear optical polarization dynamics. Zbl 1211.37097David, D.; Holm, D. D.; Tratnik, M. V. 20 1990 Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics. Zbl 1402.76101Cotter, C. J.; Gottwald, G. A.; Holm, D. D. 20 2017 Multisymplectic formulation of fluid dynamics using the inverse map. Zbl 1129.37036Cotter, C. J.; Holm, D. D.; Hydon, P. E. 19 2007 Lagrangian reduction, the Euler-Poincaré equations, and semidirect products. Zbl 0989.37052Cendra, Hernán; Holm, Darryl D.; Marsden, Jerrold E.; Ratiu, Tudor S. 19 1998 Numerically modeling stochastic Lie transport in fluid dynamics. Zbl 1454.76064Cotter, Colin; Crisan, Dan; Holm, Darryl D.; Pan, Wei; Shevchenko, Igor 19 2019 Noise and dissipation on coadjoint orbits. Zbl 1384.37063Arnaudon, Alexis; De Castro, Alex Lucio; Holm, Darryl D. 18 2018 Stepwise precession of the resonant swinging spring. Zbl 1140.37350Holm, Darryl D.; Lynch, Peter 18 2002 Long-time shallow-water equations with a varying bottom. Zbl 0897.76008Camassa, Roberto; Holm, Darryl D.; Levermore, C. David 18 1997 The ideal Craik-Leibovich equations. Zbl 0899.76082Holm, Darryl D. 18 1996 Variational principles for stochastic soliton dynamics. Zbl 1371.70041Holm, Darryl D.; Tyranowski, Tomasz M. 17 2016 Higher order Lagrange-Poincaré and Hamilton-Poincaré reductions. Zbl 1319.70022Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 17 2011 Three-dimensional stability of elliptical vortex columns in external strain flows. Zbl 0872.76041Bayly, B. J.; Holm, D. D.; Lifschitz, A. 17 1996 Euler-alpha and vortex blob regularization of vortex filament and vortex sheet motion. Zbl 1090.76015Holm, D. D.; Nitsche, M.; Putkaradze, V. 17 2006 Geometric mechanics. Part II: Rotating, translating and rolling. 2nd ed. Zbl 1381.70001Holm, Darryl D. 16 2011 Euler-Poincaré dynamics of perfect complex fluids. Zbl 1114.37308Holm, Darryl D. 16 2002 Implementation of the LANS-\(\alpha\) turbulence model in a primitive equation ocean model. Zbl 1220.86001Hecht, Matthew W.; Holm, Darryl D.; Petersen, Mark R.; Wingate, Beth A. 16 2008 Geodesic Vlasov equations and their integrable moment closures. Zbl 1190.82033Holm, Darryl D.; Tronci, Cesare 15 2009 The rotor and the pendulum. Zbl 0744.70011Holm, Darryl D.; Marsden, Jerrold E. 14 1991 Invariant higher-order variational problems. II. Zbl 1351.58009Gay-Balmaz, François; Holm, Darryl D.; Meier, David M.; Ratiu, Tudor S.; Vialard, François-Xavier 14 2012 Hamiltonian structure for two-dimensional hydrodynamics with nonlinear dispersion. Zbl 0643.76007Holm, Darryl D. 13 1988 Nonlinear stability analysis of inviscid flows in three dimensions: Incompressible fluids and barotropic fluids. Zbl 0666.76073Abarbanel, Henry D. I.; Holm, Darryl D. 13 1987 Variational principles for Lagrangian-averaged fluid dynamics. Zbl 1040.76054Holm, Darryl D. 13 2002 Momentum maps and stochastic Clebsch action principles. Zbl 1433.60069Cruzeiro, Ana Bela; Holm, Darryl D.; Ratiu, Tudor S. 13 2018 Wave breaking for the stochastic Camassa-Holm equation. Zbl 1398.35305Crisan, Dan; Holm, Darryl D. 13 2018 Stochastic geometric models with non-stationary spatial correlations in Lagrangian fluid flows. Zbl 1431.37068Gay-Balmaz, François; Holm, Darryl D. 13 2018 The analogy between spin glasses and Yang-Mills fluids. Zbl 0655.76099Holm, Darryl D.; Kupershmidt, Boris A. 12 1988 Hamiltonian formulation of the baroclinic quasigeostrophic fluid equations. Zbl 0588.76188Holm, Darryl D. 12 1986 Continuous and discrete Clebsch variational principles. Zbl 1171.37026Cotter, C. J.; Holm, D. D. 12 2009 The Maxwell-Vlasov equations in Euler-Poincaré form. Zbl 1031.76555Cendra, Hernán; Holm, Darryl D.; Hoyle, Mark J. W.; Marsden, Jerrold E. 12 1998 Lagrange-Poincaré field equations. Zbl 1253.70031Ellis, David C. P.; Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 12 2011 Complexified dynamical systems. Zbl 1120.37050Bender, Carl M.; Holm, Darryl D.; Hook, Daniel W. 12 2007 The LANS-\(\alpha \) and Leray turbulence parameterizations in primitive equation ocean modeling. Zbl 1325.76086Hecht, M. W.; Holm, D. D.; Petersen, M. R.; Wingate, B. A. 12 2008 Geodesic flows on semidirect-product Lie groups: geometry of singular measure-valued solutions. Zbl 1186.37090Holm, Darryl D.; Tronci, Cesare 11 2009 Stability of rigid body motion using the energy-Casimir method. Zbl 0526.70025Holm, Darryl; Marsden, Jerrold; Ratiu, Tudor; Weinstein, Alan 11 1984 Hamilton’s principle for quasigeostrophic motion. Zbl 1185.76848Holm, Darryl D.; Zeitlin, Vladimir 11 1998 Geometry of image registration: the diffeomorphism group and momentum maps. Zbl 1348.92094Bruveris, Martins; Holm, Darryl D. 10 2015 Complex trajectories of a simple pendulum. Zbl 1112.70020Bender, Carl M.; Holm, Darryl D.; Hook, Daniel W. 10 2007 Smooth and peaked solitons of the CH equation. Zbl 1202.35226Holm, Darryl D.; Ivanov, Rossen I. 10 2010 Hamiltonian structure and Lyapunov stability for ideal continuum dynamics. (Mathematical Seminar held at the University of Montréal, Canada, July 29 - August 16, 1985). Zbl 0594.00020Holm, D. D.; Marsden, J. E.; Ratiu, T. S. 10 1986 On billiard solutions of nonlinear PDEs. Zbl 0944.37032Alber, Mark S.; Camassa, Roberto; Fedorov, Yuri N.; Holm, Darryl D.; Marsden, Jerrold E. 10 1999 Waltzing peakons and compacton pairs in a cross-coupled Camassa-Holm equation. Zbl 1225.35198Cotter, Colin J.; Holm, Darryl D.; Ivanov, Rossen I.; Percival, James R. 10 2011 Estimates for the LANS-\(\alpha\), Leray-\(\alpha\) and Bardina models in terms of a Navier-Stokes Reynolds number. Zbl 1157.76009Gibbon, J. D.; Holm, D. D. 10 2008 Stochastic discrete Hamiltonian variational integrators. Zbl 06989587Holm, Darryl D.; Tyranowski, Tomasz M. 10 2018 Elliptical vortices and integrable Hamiltonian dynamics of the rotating shallow-water equations. Zbl 0850.76791Holm, Darryl D. 9 1991 Kármán-Howarth theorem for the Lagrangian-averaged Navier-Stokes-alpha model of turbulence. Zbl 1064.76058Holm, Darryl D. 9 2002 Extended-geostrophic Hamiltonian models for rotating shallow water motion. Zbl 0899.76080Allen, J. S.; Holm, Darryl D. 9 1996 Hamiltonian balance equations. Zbl 0900.76719Holm, Darryl D. 9 1996 Three regularization models of the Navier-Stokes equations. Zbl 1182.76288Graham, Jonathan Pietarila; Holm, Darryl D.; Mininni, Pablo D.; Pouquet, Annick 9 2008 Vlasov moments, integrable systems and singular solutions. Zbl 1217.82053Gibbons, John; Holm, Darryl D.; Tronci, Cesare 9 2008 Helicity in the formation of turbulence. Zbl 1146.76414Holm, D. D.; Kerr, R. M. 9 2007 Selective decay by Casimir dissipation in inviscid fluids. Zbl 1322.76036Gay-Balmaz, François; Holm, Darryl D. 8 2013 Integrable vs. nonintegrable geodesic soliton behavior. Zbl 0980.35134Fringer, Oliver B.; Holm, Darryl D. 8 2001 Stochastic wave-current interaction in thermal shallow water dynamics. Zbl 1468.76014Holm, Darryl D.; Luesink, Erwin 2 2021 Implications of Kunita-Itô-Wentzell formula for \(k\)-forms in stochastic fluid dynamics. Zbl 1448.70059Bethencourt de Léon, Aythami; Holm, Darryl D.; Luesink, Erwin; Takao, So 6 2020 Data assimilation for a quasi-geostrophic model with circulation-preserving stochastic transport noise. Zbl 1444.62134Cotter, Colin; Crisan, Dan; Holm, Darryl; Pan, Wei; Shevchenko, Igor 6 2020 A particle filter for stochastic advection by Lie transport: a case study for the damped and forced incompressible two-dimensional Euler equation. Zbl 1454.62528Cotter, Colin; Crisan, Dan; Holm, Darryl D.; Pan, Wei; Shevchenko, Igor 5 2020 Lagrangian averaged stochastic advection by Lie transport for fluids. Zbl 1471.76024Drivas, Theodore D.; Holm, Darryl D.; Leahy, James-Michael 3 2020 Predicting uncertainty in geometric fluid mechanics. Zbl 1439.49083Gay-Balmaz, François; Holm, Darryl D. 3 2020 Circulation and energy theorem preserving stochastic fluids. Zbl 1464.76023Drivas, Theodore D.; Holm, Darryl D. 3 2020 Modelling the climate and weather of a 2D Lagrangian-averaged Euler-Boussinesq equation with transport noise. Zbl 1446.35117Alonso-Orán, Diego; Bethencourt de León, Aythami; Holm, Darryl D.; Takao, So 2 2020 Lyapunov exponents of two stochastic Lorenz 63 systems. Zbl 1459.37066Geurts, Bernard J.; Holm, Darryl D.; Luesink, Erwin 1 2020 Solution properties of a 3D stochastic Euler fluid equation. Zbl 1433.60051Crisan, Dan; Flandoli, Franco; Holm, Darryl D. 22 2019 Numerically modeling stochastic Lie transport in fluid dynamics. Zbl 1454.76064Cotter, Colin; Crisan, Dan; Holm, Darryl D.; Pan, Wei; Shevchenko, Igor 19 2019 Stochastic parametrization of the Richardson triple. Zbl 1411.76036Holm, Darryl D. 5 2019 A geometric framework for stochastic shape analysis. Zbl 1422.60089Arnaudon, Alexis; Holm, Darryl D.; Sommer, Stefan 5 2019 Stochastic closures for wave-current interaction dynamics. Zbl 1427.76040Holm, Darryl D. 5 2019 Geometry of nonadiabatic quantum hydrodynamics. Zbl 1421.35274Foskett, Michael S.; Holm, Darryl D.; Tronci, Cesare 5 2019 Noise and dissipation on coadjoint orbits. Zbl 1384.37063Arnaudon, Alexis; De Castro, Alex Lucio; Holm, Darryl D. 18 2018 Momentum maps and stochastic Clebsch action principles. Zbl 1433.60069Cruzeiro, Ana Bela; Holm, Darryl D.; Ratiu, Tudor S. 13 2018 Wave breaking for the stochastic Camassa-Holm equation. Zbl 1398.35305Crisan, Dan; Holm, Darryl D. 13 2018 Stochastic geometric models with non-stationary spatial correlations in Lagrangian fluid flows. Zbl 1431.37068Gay-Balmaz, François; Holm, Darryl D. 13 2018 Stochastic discrete Hamiltonian variational integrators. Zbl 06989587Holm, Darryl D.; Tyranowski, Tomasz M. 10 2018 New variational and multisymplectic formulations of the Euler-Poincaré equation on the Virasoro-Bott group using the inverse map. Zbl 1402.35247Holm, Darryl D.; Tyranowski, Tomasz M. 5 2018 String methods for stochastic image and shape matching. Zbl 1455.94006Arnaudon, Alexis; Holm, Darryl; Sommer, Stefan 2 2018 Un-reduction in field theory. Zbl 1385.58008Arnaudon, Alexis; Castrillón López, Marco; Holm, Darryl D. 1 2018 Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics. Zbl 1402.76101Cotter, C. J.; Gottwald, G. A.; Holm, D. D. 20 2017 Noise and dissipation in rigid body motion. Zbl 1433.70042Arnaudon, Alexis; De Castro, Alex L.; Holm, Darryl D. 3 2017 Multipole vortex blobs (MVB): symplectic geometry and dynamics. Zbl 1365.76212Holm, Darryl D.; Jacobs, Henry O. 1 2017 \(G\)-strands on symmetric spaces. Zbl 1404.35383Arnaudon, Alexis; Holm, Darryl D.; Ivanov, Rossen I. 1 2017 Variational principles for stochastic soliton dynamics. Zbl 1371.70041Holm, Darryl D.; Tyranowski, Tomasz M. 17 2016 Weak dual pairs and jetlet methods for ideal incompressible fluid models in \(n \geq 2\) dimensions. Zbl 1368.37076Cotter, C. J.; Eldering, J.; Holm, D. D.; Jacobs, H. O.; Meier, D. M. 1 2016 Variational principles for stochastic fluid dynamics. Zbl 1371.35219Holm, Darryl D. 63 2015 Geometry of image registration: the diffeomorphism group and momentum maps. Zbl 1348.92094Bruveris, Martins; Holm, Darryl D. 10 2015 Geometry, mechanics, and dynamics. The legacy of Jerry Marsden. Selected papers presented at a focus program, Fields Institute for Research in Mathematical Sciences, Toronto, Canada, July 2012. Zbl 1317.53004 1 2015 A geometric theory of selective decay with applications in MHD. Zbl 1308.37029Gay-Balmaz, François; Holm, Darryl D. 5 2014 Matrix G-strands. Zbl 1351.37259Holm, Darryl D.; Ivanov, Rossen I. 3 2014 A jetlet hierarchy for ideal fluid dynamics. Zbl 1296.76106Cotter, C. J.; Holm, D. D.; Jacobs, H. O.; Meier, D. M. 2 2014 Integrable \(G\)-strands on semisimple Lie groups. Zbl 1298.22012Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 1 2014 Selective decay by Casimir dissipation in inviscid fluids. Zbl 1322.76036Gay-Balmaz, François; Holm, Darryl D. 8 2013 Inexact trajectory planning and inverse problems in the Hamilton-Pontryagin framework. Zbl 1371.49025Burnett, Christopher L.; Holm, Darryl D.; Meier, David M. 7 2013 On the persistence properties of the cross-coupled Camassa-Holm system. Zbl 1300.35124Henry, David; Holm, Darryl; Ivanov, Rossen 7 2013 Geometric dynamics of optimization. Zbl 1271.49003Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 7 2013 A variational formulation of vertical slice models. Zbl 1371.86019Cotter, C. J.; Holm, D. D. 3 2013 Relative geodesics in the special Euclidean group. Zbl 1371.53035Holm, D. D.; Noakes, L.; Vankerschaver, J. 3 2013 \(G\)-strands and peakon collisions on \(\text{Diff}(\mathbb R)\). Zbl 1275.37032Holm, Darryl D.; Ivanov, Rossen I. 2 2013 Singular solutions of Euler-Poincaré equations on manifolds with symmetry. Zbl 1331.53100Holm, D. D.; Munn, J.; Stechmann, S. N. 2 2013 On Noether’s theorem for the Euler-Poincaré equation on the diffeomorphism group with advected quantities. Zbl 1352.37173Cotter, C. J.; Holm, D. D. 1 2013 Invariant higher-order variational problems. Zbl 1279.58009Gay-Balmaz, François; Holm, Darryl D.; Meier, David M.; Ratiu, Tudor S.; Vialard, François-Xavier 30 2012 Invariant higher-order variational problems. II. Zbl 1351.58009Gay-Balmaz, François; Holm, Darryl D.; Meier, David M.; Ratiu, Tudor S.; Vialard, François-Xavier 14 2012 Multiscale turbulence models based on convected fluid microstructure. Zbl 1426.76195Holm, Darryl D.; Tronci, Cesare 7 2012 \(G\)-strands. Zbl 1339.37048Holm, Darryl D.; Ivanov, Rossen I.; Percival, James R. 5 2012 Exact geometric theory of dendronized polymer dynamics. Zbl 1257.82113Gay-Balmaz, François; Holm, Darryl D.; Putkaradze, Vakhtang; Ratiu, Tudor S. 3 2012 Euler-Poincaré formulation of hybrid plasma models. Zbl 1291.35404Holm, Darryl D.; Tronci, Cesare 2 2012 Stretching and folding diagnostics in solutions of the three-dimensional Euler and Navier-Stokes equations. Zbl 1296.35130Gibbon, John D.; Holm, Darryl D. 1 2012 Two-component CH system: inverse scattering, peakons and geometry. Zbl 1216.35175Holm, D. D.; Ivanov, R. I. 29 2011 Geometric mechanics. Part I: Dynamics and symmetry. 2nd ed. Zbl 1227.70001Holm, Darryl D. 25 2011 The momentum map representation of images. Zbl 1211.58010Bruveris, M.; Gay-Balmaz, F.; Holm, D. D.; Ratiu, T. S. 23 2011 Higher order Lagrange-Poincaré and Hamilton-Poincaré reductions. Zbl 1319.70022Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 17 2011 Geometric mechanics. Part II: Rotating, translating and rolling. 2nd ed. Zbl 1381.70001Holm, Darryl D. 16 2011 Lagrange-Poincaré field equations. Zbl 1253.70031Ellis, David C. P.; Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 12 2011 Waltzing peakons and compacton pairs in a cross-coupled Camassa-Holm equation. Zbl 1225.35198Cotter, Colin J.; Holm, Darryl D.; Ivanov, Rossen I.; Percival, James R. 10 2011 The effect of subfilter-scale physics on regularization models. Zbl 1317.76051Graham, Jonathan Pietarila; Holm, Darryl D.; Mininni, Pablo; Pouquet, Annick 6 2011 Un-reduction. Zbl 1268.37081Bruveris, Martins; Ellis, David C. P.; Holm, Darryl D.; Gay-Balmaz, François 5 2011 Smooth and peaked solutions of the Camassa-Holm equation and applications. Zbl 1231.35167Holm, Darryl; Ivanov, Rossen 4 2011 Helical states of nonlocally interacting molecules and their linear stability: a geometric approach. Zbl 1208.81237Benoit, S.; Holm, D. D.; Putkaradze, V. 3 2011 Extreme events in solutions of hydrostatic and non-hydrostatic climate models. Zbl 1219.86004Gibbon, J. D.; Holm, D. D. 2 2011 Multi-component generalizations of the CH equation: geometrical aspects, peakons and numerical examples. Zbl 1213.37097Holm, D. D.; Ivanov, R. I. 28 2010 Symmetry reduced dynamics of charged molecular strands. Zbl 1333.70029Ellis, David C. P.; Gay-Balmaz, François; Holm, Darryl D.; Putkaradze, Vakhtang; Ratiu, Tudor S. 24 2010 Smooth and peaked solitons of the CH equation. Zbl 1202.35226Holm, Darryl D.; Ivanov, Rossen I. 10 2010 The square root depth wave equations. Zbl 1211.76028Cotter, C. J.; Holm, D. D.; Percival, J. R. 6 2010 Geodesic boundary value problems with symmetry. Zbl 1375.49032Cotter, Colin J.; Holm, Darryl D. 5 2010 The dynamics of the gradient of potential vorticity. Zbl 1278.76017Gibbon, J. D.; Holm, D. D. 5 2010 Double-bracket dissipation in kinetic theory for particles with anisotropic interactions. Zbl 1211.82046Holm, D. D.; Putkaradze, V.; Tronci, C. 4 2010 Geometric mechanics and symmetry. From finite to infinite dimensions. Zbl 1175.70001Holm, Darryl D.; Schmah, Tanya; Stoica, Cristina 73 2009 The Euler-Poincaré theory of metamorphosis. Zbl 1186.68413Holm, Darryl D.; Trouvé, Alain; Younes, Laurent 22 2009 Geodesic Vlasov equations and their integrable moment closures. Zbl 1190.82033Holm, Darryl D.; Tronci, Cesare 15 2009 Continuous and discrete Clebsch variational principles. Zbl 1171.37026Cotter, C. J.; Holm, D. D. 12 2009 Geodesic flows on semidirect-product Lie groups: geometry of singular measure-valued solutions. Zbl 1186.37090Holm, Darryl D.; Tronci, Cesare 11 2009 Variational principles for spin systems and the Kirchhoff rod. Zbl 1288.70012Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 8 2009 Nonlocal orientation-dependent dynamics of charged strands and ribbons. Zbl 1170.74020Holm, Darryl D.; Putkaradze, Vakhtang 8 2009 Euler’s fluid equations: Optimal control vs optimization. Zbl 1234.76008Holm, Darryl D. 1 2009 Geometric mechanics. Part I: Dynamics and symmetry. Zbl 1160.70001Holm, Darryl D. 26 2008 Geometric mechanics. Part II: Rotating, translating and rolling. Zbl 1149.70001Holm, Darryl D. 23 2008 Implementation of the LANS-\(\alpha\) turbulence model in a primitive equation ocean model. Zbl 1220.86001Hecht, Matthew W.; Holm, Darryl D.; Petersen, Mark R.; Wingate, Beth A. 16 2008 The LANS-\(\alpha \) and Leray turbulence parameterizations in primitive equation ocean modeling. Zbl 1325.76086Hecht, M. W.; Holm, D. D.; Petersen, M. R.; Wingate, B. A. 12 2008 Estimates for the LANS-\(\alpha\), Leray-\(\alpha\) and Bardina models in terms of a Navier-Stokes Reynolds number. Zbl 1157.76009Gibbon, J. D.; Holm, D. D. 10 2008 Three regularization models of the Navier-Stokes equations. Zbl 1182.76288Graham, Jonathan Pietarila; Holm, Darryl D.; Mininni, Pablo D.; Pouquet, Annick 9 2008 Vlasov moments, integrable systems and singular solutions. Zbl 1217.82053Gibbons, John; Holm, Darryl D.; Tronci, Cesare 9 2008 Geometry of Vlasov kinetic moments: a bosonic Fock space for the symmetric Schouten bracket. Zbl 1221.82102Gibbons, John; Holm, Darryl D.; Tronci, Cesare 7 2008 Geometric gradient-flow dynamics with singular solutions. Zbl 1155.76007Holm, Darryl D.; Putkaradze, Vakhtang; Tronci, Cesare 5 2008 A Euler-Poincaré framework for the multilayer Green-Nagdhi equations. Zbl 1143.76021Percival, J. R.; Cotter, C. J.; Holm, D. D. 4 2008 Singular solutions for geodesic flows of Vlasov moments. Zbl 1180.82173Gibbons, John; Holm, Darryl D.; Tronci, Cesare 2 2008 Hamiltonian statistical mechanics. Zbl 1153.82011Brody, Dorje C.; Ellis, David C. P.; Holm, Darryl D. 1 2008 Kinetic models of oriented self-assembly. Zbl 1195.82070Holm, Darryl D.; Putkaradze, Vakhtang; Tronci, Cesare 1 2008 Multisymplectic formulation of fluid dynamics using the inverse map. Zbl 1129.37036Cotter, C. J.; Holm, D. D.; Hydon, P. E. 19 2007 Complexified dynamical systems. Zbl 1120.37050Bender, Carl M.; Holm, Darryl D.; Hook, Daniel W. 12 2007 Complex trajectories of a simple pendulum. Zbl 1112.70020Bender, Carl M.; Holm, Darryl D.; Hook, Daniel W. 10 2007 Helicity in the formation of turbulence. Zbl 1146.76414Holm, D. D.; Kerr, R. M. 9 2007 Lagrangian particle paths and ortho-normal quaternion frames. Zbl 1118.76017Gibbon, J. D.; Holm, D. D. 5 2007 Geometric dissipation in kinetic equations. Zbl 1174.82010Holm, Darryl D.; Putkaradze, Vakhtang; Tronci, Cesare 4 2007 Formation and evolution of singularities in anisotropic geometric continua. Zbl 1155.35411Holm, D. D.; Putkaradze, V. 3 2007 Leray and LANs-\(\alpha\) modelling of turbulent mixing. Zbl 1273.76139Geurts, Bernard J.; Holm, Darryl D. 38 2006 ...and 102 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,862 Authors 104 Holm, Darryl D. 93 Yin, Zhaoyang 51 Liu, Yue 46 Qiao, Zhijun 43 Tian, Lixin 42 Gay-Balmaz, François 42 Marsden, Jerrold Eldon 36 Ratiu, Tudor Stefan 30 Mu, Chunlai 30 Zhou, Shouming 29 Liu, Zhengrong 29 Qu, Changzheng 28 Li, Jibin 26 Guo, Boling 26 Rebholz, Leo G. 26 Titi, Edriss Saleh 25 Lai, Shaoyong 25 Mi, Yongsheng 24 Gao, Hongjun 22 Constantin, Adrian 22 Guo, Zhengguang 21 Himonas, A. Alexandrou 20 Lenells, Jonatan 20 Tronci, Cesare 18 Cotter, Colin John 18 Escher, Joachim 18 Liu, Xingxing 18 Putkaradze, Vakhtang 17 Ivanov, Rossen I. 16 Chen, Aiyong 16 Fu, Ying 16 Szmigielski, Jacek 16 Yan, Kai 16 Yan, Wei 15 Kolev, Boris 15 Li, Yongsheng 15 Zhu, Min 14 Duan, Jinqiao 14 Gui, Guilong 14 Holden, Helge 14 Shen, Chunyu 14 Zhou, Yong 13 Guan, Chunxia 13 Guo, Fei 13 Wu, Xinglong 12 Carrillo de la Plata, José Antonio 12 Chen, Robin Ming 12 Coclite, Giuseppe Maria 12 Colombo, Leonardo Jesus 12 Hu, Qiaoyi 12 Jiang, Zaihong 12 Layton, William J. 12 Moon, Byungsoo 11 Bauer, Martin 11 Bloch, Anthony Michael 11 Camassa, Roberto 11 Grunert, Katrin 11 Guha, Partha 11 Li, Jinlu 11 Neda, Monika 11 Raynaud, Xavier 11 Sheu, Tony Wen-Hann 11 Tang, Hao 11 Vialard, François-Xavier 10 Arnaudon, Alexis 10 Eckhardt, Jonathan 10 Esen, Oğul 10 Hernández-Bermejo, Benito 10 Kupershmidt, Boris A. 10 Lăzureanu, Cristian 10 Lewandowski, Roger 10 Liu, Xiaochuan 10 Misiołek, Gerard 10 Oliver, Marcel 10 Preston, Stephen C. 10 Yang, Shaojie 10 Zhu, Mingxuan 9 Boutet de Monvel, Anne Marie 9 Chang, Xiangke 9 Chen, Guanrong 9 Deugoue, Gabriel 9 Freire, Igor Leite 9 Fried, Eliot 9 Gibbon, John D. 9 Huang, Wentao 9 Martín de Diego, David 9 Mininni, Pablo D. 9 Olver, Peter John 9 Razafimandimby, Paul André 9 Sango, Mamadou 9 Shepelsky, Dmitry 9 Yin, Jiuli 8 Anco, Stephen C. 8 Berselli, Luigi Carlo 8 Bruveris, Martins 8 Chen, Jinbing 8 Geurts, Bernard J. 8 Geyer, Anna 8 Ionescu-Kruse, Delia 8 Karlsen, Kenneth Hvistendahl ...and 2,762 more Authors all top 5 Cited in 337 Serials 178 Journal of Mathematical Physics 146 Journal of Differential Equations 132 Physica D 114 Journal of Mathematical Analysis and Applications 94 Nonlinear Analysis. 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Zeitschrift für angewandte Mathematik und Physik 19 Communications in Partial Differential Equations 19 International Journal of Geometric Methods in Modern Physics 18 Physics Letters. A 18 Theoretical and Mathematical Physics 18 Journal of Dynamics and Differential Equations 17 Journal of Statistical Physics 17 Journal of Computational and Applied Mathematics 17 Communications in Nonlinear Science and Numerical Simulation 16 Nonlinearity 15 Computers & Mathematics with Applications 15 Mathematical Methods in the Applied Sciences 15 SIAM Journal on Mathematical Analysis 15 Mathematical Problems in Engineering 15 Discrete and Continuous Dynamical Systems. Series B 15 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 14 Letters in Mathematical Physics 14 Wave Motion 14 Annales de l’Institut Henri Poincaré. 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Académie des Sciences, Paris 10 Journal of Hyperbolic Differential Equations 10 Advances in Difference Equations 10 SIAM Journal on Imaging Sciences 9 Mathematics and Computers in Simulation 9 Applied Numerical Mathematics 9 Journal of Scientific Computing 9 Applied Mathematical Modelling 9 Calculus of Variations and Partial Differential Equations 9 Journal of Inequalities and Applications 9 Qualitative Theory of Dynamical Systems 9 Foundations of Computational Mathematics 9 Journal of Applied Mathematics 9 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 8 Geophysical and Astrophysical Fluid Dynamics 8 Annali di Matematica Pura ed Applicata. Serie Quarta 8 Acta Mathematicae Applicatae Sinica. English Series 8 NoDEA. Nonlinear Differential Equations and Applications 8 European Journal of Mechanics. B. Fluids 8 Discrete and Continuous Dynamical Systems. Series S 8 Journal of Applied Analysis and Computation 7 Computer Methods in Applied Mechanics and Engineering 7 Applied Mathematics and Optimization 7 Numerical Functional Analysis and Optimization 7 Stochastic Processes and their Applications 7 Journal of Mathematical Imaging and Vision 7 Mathematical Physics, Analysis and Geometry 7 Journal of Turbulence 7 Analysis and Applications (Singapore) 6 Communications on Pure and Applied Mathematics 6 International Journal of Theoretical Physics 6 Physics Reports 6 BIT 6 Proceedings of the American Mathematical Society 6 Dynamics and Stability of Systems 6 Computational Mathematics and Mathematical Physics ...and 237 more Serials all top 5 Cited in 54 Fields 1,949 Partial differential equations (35-XX) 1,066 Fluid mechanics (76-XX) 777 Dynamical systems and ergodic theory (37-XX) 327 Mechanics of particles and systems (70-XX) 229 Numerical analysis (65-XX) 169 Ordinary differential equations (34-XX) 149 Differential geometry (53-XX) 133 Global analysis, analysis on manifolds (58-XX) 103 Geophysics (86-XX) 102 Probability theory and stochastic processes (60-XX) 101 Mechanics of deformable solids (74-XX) 94 Statistical mechanics, structure of matter (82-XX) 85 Calculus of variations and optimal control; optimization (49-XX) 59 Quantum theory (81-XX) 57 Systems theory; control (93-XX) 41 Operator theory (47-XX) 40 Biology and other natural sciences (92-XX) 31 Topological groups, Lie groups (22-XX) 27 Computer science (68-XX) 26 Nonassociative rings and algebras (17-XX) 25 Optics, electromagnetic theory (78-XX) 25 Information and communication theory, circuits (94-XX) 24 Real functions (26-XX) 24 Classical thermodynamics, heat transfer (80-XX) 21 Relativity and gravitational theory (83-XX) 19 Harmonic analysis on Euclidean spaces (42-XX) 15 Functional analysis (46-XX) 14 Functions of a complex variable (30-XX) 14 Statistics (62-XX) 13 Special functions (33-XX) 11 Integral equations (45-XX) 8 Astronomy and astrophysics (85-XX) 7 Algebraic geometry (14-XX) 7 Difference and functional equations (39-XX) 5 Measure and integration (28-XX) 5 Approximations and expansions (41-XX) 5 Operations research, mathematical programming (90-XX) 4 General and overarching topics; collections (00-XX) 4 History and biography (01-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Manifolds and cell complexes (57-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Integral transforms, operational calculus (44-XX) 2 Commutative algebra (13-XX) 2 Group theory and generalizations (20-XX) 2 General topology (54-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Geometry (51-XX) 1 Algebraic topology (55-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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