Edit Profile Agrachev, Andreĭ Aleksandrovich Compute Distance To: Compute Author ID: agrachev.andrej-a Published as: Agrachev, A.; Agrachev, A. A.; Agrachev, Andrei; Agrachev, Andrei A.; Agrachev, Andrej A.; Agrachev, Andrey; Agrachev, Andrey A.; Agrachëv, A. A.; Agrachě, A. A. Homepage: http://people.sissa.it/~agrachev/ External Links: MGP · Math-Net.Ru · Wikidata · ResearchGate Documents Indexed: 148 Publications since 1975, including 5 Books Biographic References: 1 Publication all top 5 Co-Authors 30 single-authored 36 Gamkrelidze, Revaz Valerianovich 11 Vakhrameev, S. A. 10 Gauthier, Jean-Paul A. 10 Sarychev, Andrei V. 8 Boscain, Ugo 7 Barilari, Davide 5 Sarychev, Andrey V. 5 Stefani, Gianna 5 Zelenko, Igor 5 Zezza, Pierluigi 4 Lee, Paul W. Y. 4 Rizzi, Luca 4 Sigalotti, Mario 3 Anosov, Dmitriĭ Viktorovich 3 Biolo, Carolina 3 Charlot, Grégoire 3 Lerario, Antonio 3 Ostianu, N. M. 3 Sakharova, V. P. 2 Arutyunov, Aram Vladimirovic 2 Aseev, Sergei M. 2 Avakov, Evgeniĭ Rachievich 2 Baryshnikov, Yuliy M. 2 Beschastnyi, Ivan Yu. 2 Caponigro, Marco 2 Chittaro, Francesca C. 2 Davydov, Alekseĭ Aleksandrovich 2 Kupka, Ivan A. K. 2 Liberzon, Daniel 2 Marigo, Alessia 2 Sachkov, Yuriĭ Leonidovich 2 Treshchev, Dmitriĭ Valer’evich 2 Zakalyukin, Vladimir M. 1 Besov, Konstantin O. 1 Boarotto, Francesco 1 Bogaevskij, Il’ya Aleksandrovich 1 Bonnard, Bernard 1 Bortakovskii, A. S. 1 Budak, A. B. 1 Bukhshtaber, Viktor Matveevich 1 Chakir El-A., El-H. 1 Chambrion, Thomas 1 Chubarikov, Vladimir Nikolaevich 1 Chyba, Monique 1 El Alaoui, El-Houcine Chakir 1 Faddeev, Lyudvig Dmitrievich 1 Gentile, Alessandro 1 Ghezzi, Roberta 1 Gonchar, Andreĭ Aleksandrovich 1 Goryunov, Victor V. 1 Grigorenko, Nikolaĭ Leont’evich 1 Gusein-Zade, Sabir M. 1 Kaimanovich, Vadim A. 1 Kashin, Boris Sergeevich 1 Kolesov, Andreĭ Yur’evich 1 Konovalov, S. P. 1 Kozhasov, Khazhgali 1 Kozlov, Valeriĭ Vasil’evich 1 Krasovskiĭ, Nikolaĭ Nikolaevich 1 Kryazhimskiĭ, Arkadiĭ Viktorovich 1 Kuksin, Sergeĭ B. 1 Kurzhanskiĭ, Aleksandr Borisovich 1 Lysenok, Igor’ Geront’evich 1 Mal’tsev, Arkadiĭ Anatol’evich 1 Mishchenko, Evgeniĭ Frolovich 1 Neel, Robert Weston 1 Nikol’skiĭ, Mikhaĭl Sergeevich 1 Novikov, Sergeĭ Petrovich 1 Ol’shanskiĭ, Aleksandr Yur’evich 1 Osipov, Yuriĭ Sergeevich 1 Pallaschke, Diethard 1 Paoli, Elisa 1 Remeslennikov, Vladimir Nikanorovich 1 Rossi, Francesco 1 Rozov, Nikolaĭ Khristovich 1 Scholtes, Stefan 1 Sedykh, Vyacheslav Dmitrievich 1 Sergeev, Armen Glebovich 1 Shchepin, Evgenij V. 1 Shcherbakova, Nataliya 1 Shirikyan, Armen R. 1 Silveira, Pavel 1 Sinaĭ, Yakov Grigor’evich 1 Smirnov, Stanislav Konstantinovich 1 Stepin, Anatolii Mikhailovich 1 Taimanov, Iskander Asanovich 1 Uschmajew, André 1 Vasil’ev, Viktor Anatol’evich 1 Vershik, Anatoliĭ Moiseevich 1 Vladimirov, Vasiliĭ Sergeevich 1 Volkov, Evgeniĭ Alekseevich 1 Vorobets, Ya. B. 1 Zarodov, V. R. 1 Zelikin, Mikhail Il’ich 1 Zhizhchenko, Alexey B. all top 5 Serials 18 Journal of Dynamical and Control Systems 8 Journal of Soviet Mathematics 6 Russian Mathematical Surveys 6 SIAM Journal on Control and Optimization 6 Soviet Mathematics. Doklady 6 Mathematics of the USSR, Sbornik 6 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 6 Proceedings of the Steklov Institute of Mathematics 5 Journal of Mathematical Sciences (New York) 5 Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Matematicheskiĭ Sbornik. Novaya Seriya 3 Acta Applicandae Mathematicae 3 Calculus of Variations and Partial Differential Equations 3 Doklady Mathematics 2 Systems & Control Letters 2 The Journal of Geometric Analysis 2 Matematicheskiĭ Sbornik 1 Communications in Mathematical Physics 1 International Journal of Control 1 Mathematical Notes 1 Annales de l’Institut Fourier 1 Functional Analysis and its Applications 1 Journal of Functional Analysis 1 Mathematische Annalen 1 Memoirs of the American Mathematical Society 1 Proceedings of the London Mathematical Society. Third Series 1 Transactions of the American Mathematical Society 1 Rendiconti del Seminario Matematico 1 SIAM Journal on Matrix Analysis and Applications 1 Problems of Control and Information Theory 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Journal of Mathematical Systems, Estimation, and Control 1 Electronic Research Announcements of the American Mathematical Society 1 Discrete and Continuous Dynamical Systems 1 Bulletin of the Georgian Academy of Sciences 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Geometry & Topology 1 Journal of Mathematical Fluid Mechanics 1 Regular and Chaotic Dynamics 1 Cambridge Studies in Advanced Mathematics 1 ICPT Lecture Notes 1 Arnold Mathematical Journal all top 5 Fields 63 Calculus of variations and optimal control; optimization (49-XX) 55 Systems theory; control (93-XX) 54 Differential geometry (53-XX) 40 Global analysis, analysis on manifolds (58-XX) 23 Dynamical systems and ergodic theory (37-XX) 8 Ordinary differential equations (34-XX) 8 Partial differential equations (35-XX) 6 Topological groups, Lie groups (22-XX) 6 Manifolds and cell complexes (57-XX) 6 Mechanics of particles and systems (70-XX) 5 History and biography (01-XX) 5 Functional analysis (46-XX) 4 General and overarching topics; collections (00-XX) 4 Nonassociative rings and algebras (17-XX) 3 Algebraic geometry (14-XX) 3 Algebraic topology (55-XX) 3 Fluid mechanics (76-XX) 3 Operations research, mathematical programming (90-XX) 2 Group theory and generalizations (20-XX) 2 Real functions (26-XX) 2 Probability theory and stochastic processes (60-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Abstract harmonic analysis (43-XX) 1 Operator theory (47-XX) 1 General topology (54-XX) 1 Numerical analysis (65-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 124 Publications have been cited 1,837 times in 991 Documents Cited by ▼ Year ▼ Control theory from the geometric viewpoint. Zbl 1062.93001Agrachev, Andrei A.; Sachkov, Yuri L. 347 2004 Lie-algebraic stability criteria for switched systems. Zbl 0995.93064Agrachev, Andrei A.; Liberzon, Daniel 75 2001 The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups. Zbl 1165.58012Agrachev, Andrei; Boscain, Ugo; Gauthier, Jean-Paul; Rossi, Francesco 56 2009 Introduction to geodesics in sub-Riemannian geometry. Zbl 1362.53001Agrachev, Andrei; Barilari, Davide; Boscain, Ugo 54 2016 Geometric control theory. Zbl 1078.93001Agrachev, A. A.; Sachkov, Yu. L. 45 2004 Exponential representation of flows and chronological calculus. Zbl 0408.34044Agrachev, A. A.; Gamkrelidze, R. V. 44 1978 On the Hausdorff volume in sub-Riemannian geometry. Zbl 1236.53030Agrachev, Andrei; Barilari, Davide; Boscain, Ugo 41 2012 Sub-Riemannian structures on 3D Lie groups. Zbl 1244.53039Agrachev, A.; Barilari, D. 40 2012 Local invariants of smooth control systems. Zbl 0681.49018Agrachev, A. A.; Gamkrelidze, R. V.; Sarychev, A. V. 39 1989 Chronological algebras and nonstationary vector fields. Zbl 0473.58021Agrachev, A. A.; Gamkrelidze, R. V. 39 1980 Feedback-invariant optimal control theory and differential geometry. I: Regular extremals. Zbl 0952.49019Agrachev, A. A.; Gamkrelidze, R. V. 38 1997 Abnormal sub-Riemannian geodesics: Morse index and rigidity. Zbl 0866.58023Agrachev, A. A.; Sarychev, A. V. 35 1996 Geometry of Jacobi curves. I. Zbl 1019.53038Agrachev, A. A.; Zelenko, I. 33 2002 Sub-Riemannian sphere in Martinet flat case. Zbl 0902.53033Agrachev, A.; Bonnard, B.; Chyba, M.; Kupka, I. 31 1997 Exponential mappings for contact sub-Riemannian structures. Zbl 0941.53022Agrachev, A. A. 31 1996 Strong optimality for a bang-bang trajectory. Zbl 1020.49021Agrachev, Andrei A.; Stefani, Gianna; Zezza, Pierluigi 29 2002 Navier-Stokes equations: controllability by means of low modes forcing. Zbl 1075.93014Agrachev, Andrey A.; Sarychev, Andrey V. 28 2005 A comprehensive introduction to sub-Riemannian geometry. From the Hamiltonian viewpoint. With an appendix by Igor Zelenko. Zbl 07073879Agrachev, Andrei; Barilari, Davide; Boscain, Ugo 27 2020 A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds. Zbl 1198.49041Agrachev, Andrei; Boscain, Ugo; Sigalotti, Mario 27 2008 Sub-Riemannian curvature in contact geometry. Zbl 1376.53059Agrachev, Andrei; Barilari, Davide; Rizzi, Luca 23 2017 Any sub-Riemannian metric has points of smoothness. Zbl 1253.53029Agrachev, A. A. 23 2009 Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds. Zbl 1327.53032Agrachev, Andrei; Lee, Paul W. Y. 20 2014 On the local structure of optimal trajectories in R\(^{3}\). Zbl 1057.49027Agrachev, Andrei A.; Sigalotti, Mario 20 2003 On abnormal extremals for Lagrange variational problems. Zbl 0826.49012Agrachev, A. A.; Sarychev, A. V. 20 1995 Optimal transportation under nonholonomic constraints. Zbl 1175.49037Agrachev, Andrei; Lee, Paul 19 2009 Geometry of optimal control problems and Hamiltonian systems. Zbl 1170.49035Agrachev, A. A. 19 2008 The exponential representation of flows and the chronological calculus. Zbl 0429.34044Agrachev, A. A.; Gamkrelidze, R. V. 18 1979 Compactness for sub-Riemannian length–minimizers and subanalyticity. Zbl 1039.53038Agrachev, A. 17 1998 Two-dimensional almost-Riemannian structures with tangency points. Zbl 1192.53029Agrachev, A. A.; Boscain, U.; Charlot, G.; Ghezzi, R.; Sigalotti, M. 16 2010 Geometry of Jacobi curves. II. Zbl 1045.53051Agrachev, A. A.; Zelenko, I. 16 2002 Controllability of 2D Euler and Navier-Stokes equations by degenerate forcing. Zbl 1105.93008Agrachev, Andrey A.; Sarychev, Andrey V. 15 2006 Symplectic geometry for optimal control. Zbl 0719.49023Agrachev, A. A.; Gamkrelidze, R. V. 15 1990 Rolling balls and octonions. Zbl 1153.70010Agrachev, A. A. 14 2007 Feedback-invariant optimal control theory and differential geometry. II. Jacobi curves for singular extremals. Zbl 0972.49014Agrachev, A. A. 14 1998 Sub-Riemannian metrics on \(\mathbb{R}^3\). Zbl 0962.53022Agrachev, A. A.; Chakir El-A., El-H.; Gauthier, J. P. 14 1998 Strong minimality of abnormal geodesics for \(2\)-distributions. Zbl 0951.53029Agrachëv, A. A.; Sarychev, A. V. 14 1995 Filtrations of a Lie algebra of vector fields and nilpoint approximation of controlled systems. Zbl 0850.93106Agrachev, A. A.; Sarychev, A. V. 14 1987 Nonholonomic tangent spaces: intrinsic construction and rigid dimensions. Zbl 1068.58001Agrachev, A.; Marigo, A. 13 2003 On the subanalyticity of Carnot-Carathéodory distances. Zbl 1001.93014Agrachev, Andrei; Gauthier, Jean-Paul 13 2001 Ordinary differential equations on vector bundles and chronological calculi. Zbl 0719.58033Agrachev, A. A.; Gamkrelidze, R. V.; Vakhrameev, S. A. 13 1989 A second order optimality principle for a time-optimal problem. Zbl 0377.49014Agrachev, A. A.; Gamkrelidze, R. V. 13 1978 Some open problems. Zbl 1292.49040Agrachev, Andrei A. 12 2014 Curvature: a variational approach. Zbl 1409.49001Agrachev, Andrei A.; Barilari, Davide; Rizzi, Luca 11 2018 Systems of quadratic inequalities. Zbl 1277.14046Agrachev, A.; Lerario, A. 11 2012 On robust Lie-algebraic stability conditions for switched linear systems. Zbl 1238.93092Agrachev, Andrei A.; Baryshnikov, Yuliy; Liberzon, Daniel 11 2012 On finite-dimensional projections of distributions for solutions of randomly forced 2D Navier-Stokes equations. Zbl 1177.60059Agrachev, A.; Kuksin, S.; Sarychev, A.; Shirikyan, A. 11 2007 Symplectic methods for optimization and control. Zbl 0965.93034Agrachev, A.; Gamkrelidze, R. 11 1998 Differential-geometric and group-theoretic methods in the theory of optimal control. Zbl 0542.93045Agrachev, A. A.; Vakhrameev, S. A.; Gamkrelidze, R. V. 11 1983 Geodesics and horizontal-path spaces in Carnot groups. Zbl 1333.53043Agrachev, Andrei A.; Gentile, Alessandro; Lerario, Antonio 10 2015 Bishop and Laplacian comparison theorems on three-dimensional contact sub-Riemannian manifolds with symmetry. Zbl 1341.53058Agrachev, Andrei; Lee, Paul W. Y. 10 2015 An estimation of the controllability time for single-input systems on compact Lie groups. Zbl 1106.93006Agrachev, Andrei; Chambrion, Thomas 10 2006 Quadratic maps and smooth vector-valued functions: Euler characteristics of level sets. Zbl 0719.58013Agrachev, A. A.; Gamkrelidze, R. V. 10 1989 Sub-Riemannian metrics: Minimality of abnormal geodesics versus subanalyticity. Zbl 0978.53065Agrachev, Andrei A.; Sarychev, Andrei V. 9 1999 Methods of control theory in nonholonomic geometry. Zbl 0848.93012Agrachev, Andrej A. 9 1995 Symplectic geometry and necessary optimality conditions. Zbl 0729.49018Agrachev, A. A.; Gamkrelidze, R. V. 9 1991 Homology of intersections of real quadrics. Zbl 0696.55004Agrachev, A. A. 9 1988 On feedback classification of control-affine systems with one- and two-dimensional inputs. Zbl 1140.93018Agrachev, Andrei; Zelenko, Igor 8 2007 Rigid Carnot algebras: a classification. Zbl 1125.17002Agrachev, A.; Marigo, A. 8 2005 Quadratic mappings in geometric control theory. Zbl 1267.93035Agrachev, A. A. 8 1990 Topology of quadratic maps and Hessians of smooth maps. Zbl 0719.58006Agrachev, A. A. 8 1990 Computation of the Euler characteristic of intersections of real quadrics. Zbl 0721.55001Agrachev, A. A.; Gamkrelidze, R. V. 8 1988 On conjugate times of LQ optimal control problems. Zbl 1378.49034Agrachev, Andrei; Rizzi, Luca; Silveira, Pavel 7 2015 Controllability on the group of diffeomorphisms. Zbl 1188.93016Agrachev, A. A.; Caponigro, M. 7 2009 On sub-Riemann caustics and wave fronts for contact distributions in the three-space. Zbl 1040.58017Agrachev, A. A.; Charlot, G.; Gauthier, J. P. A.; Zakalyukin, V. M. 7 2000 An invariant second variation in optimal control. Zbl 0945.49015Agrachev, A.; Stefani, G.; Zezza, P. 7 1998 On Morse theory for piecewise smooth functions. Zbl 0951.49024Agrachev, A. A.; Pallaschke, D.; Scholtes, S. 7 1997 Quadratic maps and smooth vector-valued functions: Euler characteristics of level sets. Zbl 0727.58009Agrachev, A. A.; Gamkrelidze, R. V. 7 1991 The index of extremality and quasiextremal controls. Zbl 0587.49018Agrachev, A. A.; Gamkrelidze, R. V. 7 1985 The control of rotation for asymmetric rigid body. Zbl 0571.70030Agrachev, A. A.; Sarychev, A. V. 7 1983 Ensemble controllability by Lie algebraic methods. Zbl 1350.93014Agrachev, Andrei; Baryshnikov, Yuliy; Sarychev, Andrey 6 2016 On the space of symmetric operators with multiple ground states. Zbl 1271.46056Agrachev, A. A. 6 2011 Solid controllability in fluid dynamics. Zbl 1141.76026Agrachev, Andrey; Sarychev, Andrey 6 2008 The shuffle product and symmetric groups. Zbl 0790.05095Agrachev, A. A.; Gamkrelidze, R. V. 6 1994 Local controllability and semigroups of diffeomorphisms. Zbl 0787.93010Agrachev, A. A.; Gamkrelidze, R. V. 6 1993 Local controllability for families of diffeomorphisms. Zbl 0778.93003Agrachev, A. A.; Gamkrelidze, R. V. 6 1993 A second-order necessary condition for optimality in the general nonlinear case. Zbl 0386.49012Agrachev, A. A. 6 1977 On curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals. Zbl 1160.37383Agrachev, A. A.; Chtcherbakova, N. N.; Zelenko, I. 5 2005 Principal invariants of Jacobi curves. Zbl 1239.53059Agrachev, Andrei; Zelenko, Igor 5 2001 Sub-Riemannian metrics and isoperimetric problems in the contact case. Zbl 1008.53019Agrachev, A. A.; Gauthier, J. P. A. 5 2001 On the Dido problem and plane isoperimetric problems. Zbl 0977.53068Agrachev, Andrei A.; Gauthier, Jean-Paul A. 5 1999 A Hamiltonian approach to strong minima in optimal control. Zbl 0937.49012Agrachev, Andrei; Stefani, Gianna; Zezza, Pierluigi 5 1999 On regularity properties of extremal controls. Zbl 0951.49004Agrachëv, A. A. 5 1995 Newton diagrams and tangent cones to attainable sets. Zbl 0811.93006Agrachev, A. A. 5 1991 Topics in sub-Riemannian geometry. Zbl 1367.53028Agrachev, A. A. 4 2016 Volterra series and permutation groups. Zbl 0835.58030Agrachëv, A. A.; Gamkrelidze, R. V. 4 1991 Level set for a smooth mapping in the neighborhood of a singular point and zeros of a quadratic mapping. Zbl 0762.46028Avakov, E. R.; Agrachev, A. A.; Arutyunov, A. V. 4 1991 Morse theory and optimal control problems. Zbl 0743.58008Agrachev, A. A.; Vakhrameev, S. A. 4 1991 One more condition for a conditional extremum. Zbl 0693.49011Agrachev, A. A. 4 1989 The Morse index and the Maslov index for extremals of controlled systems. Zbl 0614.58016Agrachev, A. A.; Gamkrelidze, R. V. 4 1986 Chronological series and the Cauchy-Kovalevskaya theorem. Zbl 0485.35004Agrachev, A. A.; Vakhrameev, S. A. 4 1981 Homotopically invisible singular curves. Zbl 1377.53048Agrachev, Andrei A.; Boarotto, Francesco; Lerario, Antonio 3 2017 The Pontryagin maximum principle 50 years later. Zbl 1122.49001Agrachev, A. A.; Gamkrelidze, R. V. 3 2006 A “Gauss-Bonnet formula” for contact sub-Riemannian manifolds. Zbl 1044.53021Agrachev, A. A. 3 2001 Generic singularities of sub-Riemannian metrics on \(\mathbb{R}^ 3\). Zbl 0843.53025Agrachev, Andrei; El Alaoui, El-Houcine Chakir; Gauthier, Jean-Paul; Kupka, Ivan 3 1996 The level set of a smooth mapping in a neighborhood of a singular point, and zeros of a quadratic mapping. Zbl 0772.46021Avakov, E. R.; Agrachev, A. A.; Arutyunov, A. V. 3 1992 Quasi-extremality for control systems. Zbl 0721.58014Agrachev, A. A.; Gamkrelidze, R. V. 3 1989 On reduction of a smooth system linear in the control. Zbl 0678.49034Agrachev, A. A.; Sarychev, A. V. 3 1987 Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics. Zbl 1421.53037Agrachev, Andrei A.; Barilari, Davide; Paoli, Elisa 2 2019 Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling. Zbl 06996638Agrachev, Andrei; Boscain, Ugo; Neel, Robert; Rizzi, Luca 2 2018 Switching in time-optimal problem with control in a ball. Zbl 1386.49001Agrachev, Andrei A.; Biolo, Carolina 2 2018 A comprehensive introduction to sub-Riemannian geometry. From the Hamiltonian viewpoint. With an appendix by Igor Zelenko. Zbl 07073879Agrachev, Andrei; Barilari, Davide; Boscain, Ugo 27 2020 Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics. Zbl 1421.53037Agrachev, Andrei A.; Barilari, Davide; Paoli, Elisa 2 2019 Optimality of broken extremals. Zbl 1419.49013Agrachev, Andrei A.; Biolo, Carolina 1 2019 Curvature: a variational approach. Zbl 1409.49001Agrachev, Andrei A.; Barilari, Davide; Rizzi, Luca 11 2018 Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling. Zbl 06996638Agrachev, Andrei; Boscain, Ugo; Neel, Robert; Rizzi, Luca 2 2018 Switching in time-optimal problem with control in a ball. Zbl 1386.49001Agrachev, Andrei A.; Biolo, Carolina 2 2018 Sub-Riemannian curvature in contact geometry. Zbl 1376.53059Agrachev, Andrei; Barilari, Davide; Rizzi, Luca 23 2017 Homotopically invisible singular curves. Zbl 1377.53048Agrachev, Andrei A.; Boarotto, Francesco; Lerario, Antonio 3 2017 Switching in time-optimal problem: the 3D case with 2D control. Zbl 1379.49006Agrachev, Andrei A.; Biolo, Carolina 2 2017 Symplectic geometry of constrained optimization. Zbl 1408.49043Agrachev, Andrey A.; Beschastnyi, Ivan Yu. 1 2017 Introduction to geodesics in sub-Riemannian geometry. Zbl 1362.53001Agrachev, Andrei; Barilari, Davide; Boscain, Ugo 54 2016 Ensemble controllability by Lie algebraic methods. Zbl 1350.93014Agrachev, Andrei; Baryshnikov, Yuliy; Sarychev, Andrey 6 2016 Topics in sub-Riemannian geometry. Zbl 1367.53028Agrachev, A. A. 4 2016 Tangent hyperplanes to Subriemannian balls. Zbl 1351.53049Agrachev, A. A. 1 2016 Geodesics and horizontal-path spaces in Carnot groups. Zbl 1333.53043Agrachev, Andrei A.; Gentile, Alessandro; Lerario, Antonio 10 2015 Bishop and Laplacian comparison theorems on three-dimensional contact sub-Riemannian manifolds with symmetry. Zbl 1341.53058Agrachev, Andrei; Lee, Paul W. Y. 10 2015 On conjugate times of LQ optimal control problems. Zbl 1378.49034Agrachev, Andrei; Rizzi, Luca; Silveira, Pavel 7 2015 Quadratic cohomology. Zbl 1331.55003Agrachev, A. A. 2 2015 Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds. Zbl 1327.53032Agrachev, Andrei; Lee, Paul W. Y. 20 2014 Some open problems. Zbl 1292.49040Agrachev, Andrei A. 12 2014 On the Hausdorff volume in sub-Riemannian geometry. Zbl 1236.53030Agrachev, Andrei; Barilari, Davide; Boscain, Ugo 41 2012 Sub-Riemannian structures on 3D Lie groups. Zbl 1244.53039Agrachev, A.; Barilari, D. 40 2012 Systems of quadratic inequalities. Zbl 1277.14046Agrachev, A.; Lerario, A. 11 2012 On robust Lie-algebraic stability conditions for switched linear systems. Zbl 1238.93092Agrachev, Andrei A.; Baryshnikov, Yuliy; Liberzon, Daniel 11 2012 On the space of symmetric operators with multiple ground states. Zbl 1271.46056Agrachev, A. A. 6 2011 The geometry of maximum principle. Zbl 1227.49026Agrachev, A. A.; Gamkrelidze, R. V. 2 2011 Two-dimensional almost-Riemannian structures with tangency points. Zbl 1192.53029Agrachev, A. A.; Boscain, U.; Charlot, G.; Ghezzi, R.; Sigalotti, M. 16 2010 Invariant Lagrangian submanifolds of dissipative systems. Zbl 1233.37030Agrachev, A. A. 2 2010 Continuity of optimal control costs and its application to weak KAM theory. Zbl 1203.49041Agrachev, Andrei; Lee, Paul W. Y. 2 2010 In memory of Evgenii Frolovich Mishchenko. Zbl 1302.01048Osipov, Yu. S.; Kozlov, V. V.; Faddeev, L. D.; Anosov, D. V.; Vladimirov, V. S.; Gamkrelidze, R. V.; Gonchar, A. A.; Krasovskii, N. N.; Kryazhimskii, A. V.; Kurzhanski, A. B.; Novikov, S. P.; Aseev, S. M.; Zhizhchenko, A. B.; Treschev, D. V.; Agrachev, A. A.; Volkov, E. A.; Grigorenko, N. L.; Davydov, A. A.; Zelikin, M. I.; Kolesov, A. Yu.; Mal’tsev, A. A.; Nikol’skii, M. S.; Rozov, N. Kh.; Sergeev, A. G.; Besov, K. O.; Konovalov, S. P. 1 2010 Dynamics control by a time-varying feedback. Zbl 1203.93046Agrachev, A. A.; Caponigro, M. 1 2010 The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups. Zbl 1165.58012Agrachev, Andrei; Boscain, Ugo; Gauthier, Jean-Paul; Rossi, Francesco 56 2009 Any sub-Riemannian metric has points of smoothness. Zbl 1253.53029Agrachev, A. A. 23 2009 Optimal transportation under nonholonomic constraints. Zbl 1175.49037Agrachev, Andrei; Lee, Paul 19 2009 Controllability on the group of diffeomorphisms. Zbl 1188.93016Agrachev, A. A.; Caponigro, M. 7 2009 Smooth optimal synthesis for infinite horizon variational problems. Zbl 1158.49039Agrachev, Andrei A.; Chittaro, Francesca C. 1 2009 A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds. Zbl 1198.49041Agrachev, Andrei; Boscain, Ugo; Sigalotti, Mario 27 2008 Geometry of optimal control problems and Hamiltonian systems. Zbl 1170.49035Agrachev, A. A. 19 2008 Solid controllability in fluid dynamics. Zbl 1141.76026Agrachev, Andrey; Sarychev, Andrey 6 2008 Rolling balls and octonions. Zbl 1153.70010Agrachev, A. A. 14 2007 On finite-dimensional projections of distributions for solutions of randomly forced 2D Navier-Stokes equations. Zbl 1177.60059Agrachev, A.; Kuksin, S.; Sarychev, A.; Shirikyan, A. 11 2007 On feedback classification of control-affine systems with one- and two-dimensional inputs. Zbl 1140.93018Agrachev, Andrei; Zelenko, Igor 8 2007 The curvature and hyperbolicity of Hamiltonian systems. Zbl 1153.37346Agrachev, A. A. 1 2007 Controllability of 2D Euler and Navier-Stokes equations by degenerate forcing. Zbl 1105.93008Agrachev, Andrey A.; Sarychev, Andrey V. 15 2006 An estimation of the controllability time for single-input systems on compact Lie groups. Zbl 1106.93006Agrachev, Andrei; Chambrion, Thomas 10 2006 The Pontryagin maximum principle 50 years later. Zbl 1122.49001Agrachev, A. A.; Gamkrelidze, R. V. 3 2006 Vector fields on \(n\)-foliated \(2n\)-dimensional manifolds. Zbl 1244.53094Agrachev, A. A.; Gamkrelidze, R. V. 1 2006 Navier-Stokes equations: controllability by means of low modes forcing. Zbl 1075.93014Agrachev, Andrey A.; Sarychev, Andrey V. 28 2005 Rigid Carnot algebras: a classification. Zbl 1125.17002Agrachev, A.; Marigo, A. 8 2005 On curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals. Zbl 1160.37383Agrachev, A. A.; Chtcherbakova, N. N.; Zelenko, I. 5 2005 Control theory from the geometric viewpoint. Zbl 1062.93001Agrachev, Andrei A.; Sachkov, Yuri L. 347 2004 Geometric control theory. Zbl 1078.93001Agrachev, A. A.; Sachkov, Yu. L. 45 2004 Controllability of the Navier-Stokes equation by few low modes forcing. Zbl 1123.93020Agrachev, A. A.; Sarychev, A. V. 2 2004 On the local structure of optimal trajectories in R\(^{3}\). Zbl 1057.49027Agrachev, Andrei A.; Sigalotti, Mario 20 2003 Nonholonomic tangent spaces: intrinsic construction and rigid dimensions. Zbl 1068.58001Agrachev, A.; Marigo, A. 13 2003 Geometry of Jacobi curves. I. Zbl 1019.53038Agrachev, A. A.; Zelenko, I. 33 2002 Strong optimality for a bang-bang trajectory. Zbl 1020.49021Agrachev, Andrei A.; Stefani, Gianna; Zezza, Pierluigi 29 2002 Geometry of Jacobi curves. II. Zbl 1045.53051Agrachev, A. A.; Zelenko, I. 16 2002 Introduction to optimal control theory. Zbl 1034.93010Agrachev, Andrei A. 1 2002 Lie-algebraic stability criteria for switched systems. Zbl 0995.93064Agrachev, Andrei A.; Liberzon, Daniel 75 2001 On the subanalyticity of Carnot-Carathéodory distances. Zbl 1001.93014Agrachev, Andrei; Gauthier, Jean-Paul 13 2001 Principal invariants of Jacobi curves. Zbl 1239.53059Agrachev, Andrei; Zelenko, Igor 5 2001 Sub-Riemannian metrics and isoperimetric problems in the contact case. Zbl 1008.53019Agrachev, A. A.; Gauthier, J. P. A. 5 2001 A “Gauss-Bonnet formula” for contact sub-Riemannian manifolds. Zbl 1044.53021Agrachev, A. A. 3 2001 On sub-Riemann caustics and wave fronts for contact distributions in the three-space. Zbl 1040.58017Agrachev, A. A.; Charlot, G.; Gauthier, J. P. A.; Zakalyukin, V. M. 7 2000 Sub-Riemannian metrics: Minimality of abnormal geodesics versus subanalyticity. Zbl 0978.53065Agrachev, Andrei A.; Sarychev, Andrei V. 9 1999 On the Dido problem and plane isoperimetric problems. Zbl 0977.53068Agrachev, Andrei A.; Gauthier, Jean-Paul A. 5 1999 A Hamiltonian approach to strong minima in optimal control. Zbl 0937.49012Agrachev, Andrei; Stefani, Gianna; Zezza, Pierluigi 5 1999 Functional analysis - 4. Zbl 0930.00011Gamkrelidze, R. V. (ed.); Agrachev, A. A. (ed.); Vakhrameev, S. A. (ed.); Ostianu, N. M. (ed.); Sakharova, V. P. (ed.) 2 1999 Sub-Riemannian metrics and isoperimetric problems in contact case. Zbl 0986.53009Agrachev, A. A.; Gauthier, J. P. A. 1 1999 Compactness for sub-Riemannian length–minimizers and subanalyticity. Zbl 1039.53038Agrachev, A. 17 1998 Feedback-invariant optimal control theory and differential geometry. II. Jacobi curves for singular extremals. Zbl 0972.49014Agrachev, A. A. 14 1998 Sub-Riemannian metrics on \(\mathbb{R}^3\). Zbl 0962.53022Agrachev, A. A.; Chakir El-A., El-H.; Gauthier, J. P. 14 1998 Symplectic methods for optimization and control. Zbl 0965.93034Agrachev, A.; Gamkrelidze, R. 11 1998 An invariant second variation in optimal control. Zbl 0945.49015Agrachev, A.; Stefani, G.; Zezza, P. 7 1998 Strong minima in optimal control. Zbl 0936.49014Agrachev, A.; Stefani, G.; Zezza, P. 2 1998 Feedback-invariant optimal control theory and differential geometry. I: Regular extremals. Zbl 0952.49019Agrachev, A. A.; Gamkrelidze, R. V. 38 1997 Sub-Riemannian sphere in Martinet flat case. Zbl 0902.53033Agrachev, A.; Bonnard, B.; Chyba, M.; Kupka, I. 31 1997 On Morse theory for piecewise smooth functions. Zbl 0951.49024Agrachev, A. A.; Pallaschke, D.; Scholtes, S. 7 1997 Abnormal sub-Riemannian geodesics: Morse index and rigidity. Zbl 0866.58023Agrachev, A. A.; Sarychev, A. V. 35 1996 Exponential mappings for contact sub-Riemannian structures. Zbl 0941.53022Agrachev, A. A. 31 1996 Generic singularities of sub-Riemannian metrics on \(\mathbb{R}^ 3\). Zbl 0843.53025Agrachev, Andrei; El Alaoui, El-Houcine Chakir; Gauthier, Jean-Paul; Kupka, Ivan 3 1996 On abnormal extremals for Lagrange variational problems. Zbl 0826.49012Agrachev, A. A.; Sarychev, A. V. 20 1995 Strong minimality of abnormal geodesics for \(2\)-distributions. Zbl 0951.53029Agrachëv, A. A.; Sarychev, A. V. 14 1995 Methods of control theory in nonholonomic geometry. Zbl 0848.93012Agrachev, Andrej A. 9 1995 On regularity properties of extremal controls. Zbl 0951.49004Agrachëv, A. A. 5 1995 On the orbits of groups of diffeomorphisms and flows. Zbl 0902.58004Agrachev, A. A.; Gamkrelidze, R. V. 1 1995 The shuffle product and symmetric groups. Zbl 0790.05095Agrachev, A. A.; Gamkrelidze, R. V. 6 1994 Local controllability and semigroups of diffeomorphisms. Zbl 0787.93010Agrachev, A. A.; Gamkrelidze, R. V. 6 1993 Local controllability for families of diffeomorphisms. Zbl 0778.93003Agrachev, A. A.; Gamkrelidze, R. V. 6 1993 The level set of a smooth mapping in a neighborhood of a singular point, and zeros of a quadratic mapping. Zbl 0772.46021Avakov, E. R.; Agrachev, A. A.; Arutyunov, A. V. 3 1992 Symplectic geometry and necessary conditions for optimality. Zbl 0776.49014Agrachev, A. A.; Gamkrelidze, R. V. 1 1992 Symplectic geometry and necessary optimality conditions. Zbl 0729.49018Agrachev, A. A.; Gamkrelidze, R. V. 9 1991 Quadratic maps and smooth vector-valued functions: Euler characteristics of level sets. Zbl 0727.58009Agrachev, A. A.; Gamkrelidze, R. V. 7 1991 Newton diagrams and tangent cones to attainable sets. Zbl 0811.93006Agrachev, A. A. 5 1991 Volterra series and permutation groups. Zbl 0835.58030Agrachëv, A. A.; Gamkrelidze, R. V. 4 1991 Level set for a smooth mapping in the neighborhood of a singular point and zeros of a quadratic mapping. Zbl 0762.46028Avakov, E. R.; Agrachev, A. A.; Arutyunov, A. V. 4 1991 Morse theory and optimal control problems. Zbl 0743.58008Agrachev, A. A.; Vakhrameev, S. A. 4 1991 Ordinary differential equations on vector bundles and chronological calculus. Zbl 0727.58042Gamkrelidze, R. V.; Agrachev, A. A.; Vakhrameev, S. A. 2 1991 Volterra series and permutation groups. Zbl 0797.58073Agrachëv, A. A.; Gamkrelidze, R. V. 1 1991 ...and 24 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 977 Authors 58 Agrachev, Andreĭ Aleksandrovich 44 Sachkov, Yuriĭ Leonidovich 29 Boscain, Ugo 24 Trélat, Emmanuel 20 Barilari, Davide 18 Sigalotti, Mario 17 Bonnard, Bernard 17 Rizzi, Luca 14 Gauthier, Jean-Paul A. 13 Arutyunov, Aram Vladimirovic 13 Biggs, Rory 13 Gamkrelidze, Revaz Valerianovich 13 Le Donne, Enrico 13 Zelenko, Igor 12 Remsing, Claudiu-Cristian 11 Ardentov, Andrei A. 11 Chitour, Yacine 11 Grong, Erlend 11 Mashtakov, Alexey P. 11 Vakhrameev, S. A. 10 Duits, Remco 10 Lee, Paul W. Y. 9 Chittaro, Francesca C. 9 Prandi, Dario 8 Berestovskiĭ, Valeriĭ Nikolaevich 8 Boarotto, Francesco 8 Godoy Molina, Mauricio 8 Grochowski, Marek 8 Jean, Frédéric 8 Lerario, Antonio 8 Mason, Paolo 8 Poggiolini, Laura 8 Rifford, Ludovic 8 Rossi, Francesco 8 Sachkova, Elena F. 8 Sarychev, Andrej V. 7 Baudoin, Fabrice 7 Caillau, Jean-Baptiste 7 Caponigro, Marco 7 Charlot, Grégoire 7 Ebrahimi-Fard, Kurusch 7 Kokkonen, Petri 7 Manchon, Dominique 7 Margaliot, Michael 7 Markina, Irina 7 Serres, Ulysse 7 Shirikyan, Armen R. 6 Barbero-Liñán, María 6 Ghezzi, Roberta 6 Ignatovich, Svetlana Yu. 6 Karmanova, Maria B. 6 Khimshiashvili, Giorgi 6 Krasnov, Vyacheslav Alekseevich 6 Mamaev, Ivan Sergeevich 6 Neel, Robert Weston 6 Ottazzi, Alessandro 6 Podobryaev, Alekseĭ V. 6 Sarychev, Andrey V. 6 Shcherbakova, Nataliya 6 Silva Leite, Fátima 6 Tryamkin, Maksim Vladimirovich 6 Vittone, Davide 6 Zakalyukin, Vladimir M. 5 Bauer, Wolfram 5 Beschastnyi, Ivan Yu. 5 Chambrion, Thomas 5 Chyba, Monique 5 Doubrov, Boris M. 5 Furutani, Kenro 5 Gordina, Maria 5 Gupta, Rohit K. 5 Kilin, Aleksandr Aleksandrovich 5 Li, Chengbo 5 Lokutsievskiy, Lev Viacheslavovich 5 Nersesyan, Vahagn 5 Patras, Frédéric 5 Schättler, Heinz Michael 5 Speight, Gareth 5 Stefani, Gianna 4 Albano, Paolo 4 Balogh, Zoltán M. 4 Barrett, Dennis I. 4 Beauchard, Karine 4 Bekkers, Erik J. 4 Bloch, Anthony M. 4 Borisov, Alekseĭ Vladimirovich 4 Cannarsa, Piermarco 4 Cheng, Chun-Ming 4 Cheng, Daizhan 4 Chiou, Juing-Shian 4 Dirr, Gunther 4 Durán Fernandez, Carlos Eduardo 4 Gurman, Vladimir Iosifovich 4 Iwasaki, Chisato 4 Jouan, Philippe 4 Kipka, Robert J. 4 Kovalev, Alexander M. 4 Laurent, Camille 4 Liberzon, Daniel 4 Mahmudov, Elimhan N. ...and 877 more Authors all top 5 Cited in 226 Serials 95 Journal of Dynamical and Control Systems 49 Journal of Mathematical Sciences (New York) 37 SIAM Journal on Control and Optimization 34 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 28 Systems & Control Letters 24 Automatica 20 Proceedings of the Steklov Institute of Mathematics 19 Journal of Geometry and Physics 19 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 18 Journal of Differential Equations 17 Differential Equations 16 Acta Applicandae Mathematicae 16 Differential Geometry and its Applications 15 Mathematical Notes 15 Siberian Mathematical Journal 15 Automation and Remote Control 15 Calculus of Variations and Partial Differential Equations 13 Journal of Optimization Theory and Applications 13 Doklady Mathematics 12 Journal of Soviet Mathematics 12 The Journal of Geometric Analysis 12 Regular and Chaotic Dynamics 11 Journal of Mathematical Analysis and Applications 10 Journal de Mathématiques Pures et Appliquées. Neuvième Série 9 Potential Analysis 8 International Journal of Control 8 Journal of Mathematical Physics 8 Journal of Functional Analysis 8 Transactions of the American Mathematical Society 8 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Mathematische Zeitschrift 7 MCSS. Mathematics of Control, Signals, and Systems 7 Sbornik: Mathematics 7 Discrete and Continuous Dynamical Systems 7 Journal of Geometric Mechanics 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 Journal of Mathematical Imaging and Vision 6 European Journal of Control 6 Nelineĭnaya Dinamika 5 Communications in Mathematical Physics 5 Journal of the Franklin Institute 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Geometric and Functional Analysis. GAFA 5 Journal of Nonlinear Science 5 Journal of the European Mathematical Society (JEMS) 5 Nonlinear Analysis. Hybrid Systems 4 Annales de l’Institut Fourier 4 Journal of Algebra 4 Mathematische Annalen 4 Discrete & Computational Geometry 4 Revista Matemática Iberoamericana 4 Computational Mathematics and Mathematical Physics 4 Russian Mathematics 4 Abstract and Applied Analysis 4 Foundations of Computational Mathematics 4 Analysis and Geometry in Metric Spaces 4 Nonlinear Analysis. Theory, Methods & Applications 4 European Journal of Mathematics 3 Journal of Applied Mathematics and Mechanics 3 Nonlinearity 3 Advances in Mathematics 3 Applied Mathematics and Computation 3 Proceedings of the American Mathematical Society 3 Optimization 3 Journal of Global Optimization 3 Communications in Partial Differential Equations 3 NoDEA. Nonlinear Differential Equations and Applications 3 Bulletin des Sciences Mathématiques 3 Izvestiya: Mathematics 3 Mathematical Problems in Engineering 3 International Journal of Geometric Methods in Modern Physics 3 Advances in Mathematical Physics 3 Analysis and Mathematical Physics 3 Journal de l’École Polytechnique – Mathématiques 3 Mechanics of Solids 2 Communications in Algebra 2 International Journal of Systems Science 2 Israel Journal of Mathematics 2 Journal d’Analyse Mathématique 2 Letters in Mathematical Physics 2 Reports on Mathematical Physics 2 Russian Mathematical Surveys 2 Theoretical and Mathematical Physics 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Chaos, Solitons and Fractals 2 Prikladnaya Matematika i Mekhanika 2 Duke Mathematical Journal 2 Inventiones Mathematicae 2 Journal für die Reine und Angewandte Mathematik 2 Optimal Control Applications & Methods 2 Advances in Applied Mathematics 2 Chinese Annals of Mathematics. Series B 2 Applied Mathematics Letters 2 Computational Mathematics and Modeling 2 Applied Mathematical Modelling 2 Linear Algebra and its Applications 2 SIAM Journal on Applied Mathematics 2 Stochastic Processes and their Applications 2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 2 Celestial Mechanics and Dynamical Astronomy ...and 126 more Serials all top 5 Cited in 56 Fields 356 Differential geometry (53-XX) 354 Calculus of variations and optimal control; optimization (49-XX) 334 Systems theory; control (93-XX) 155 Global analysis, analysis on manifolds (58-XX) 115 Partial differential equations (35-XX) 93 Dynamical systems and ergodic theory (37-XX) 90 Ordinary differential equations (34-XX) 85 Mechanics of particles and systems (70-XX) 71 Topological groups, Lie groups (22-XX) 37 Numerical analysis (65-XX) 34 Nonassociative rings and algebras (17-XX) 34 Quantum theory (81-XX) 32 Fluid mechanics (76-XX) 29 Algebraic geometry (14-XX) 27 Probability theory and stochastic processes (60-XX) 25 Operations research, mathematical programming (90-XX) 21 Operator theory (47-XX) 20 Biology and other natural sciences (92-XX) 18 Manifolds and cell complexes (57-XX) 16 Abstract harmonic analysis (43-XX) 15 Measure and integration (28-XX) 14 Real functions (26-XX) 14 Functional analysis (46-XX) 13 Mechanics of deformable solids (74-XX) 12 Combinatorics (05-XX) 12 Several complex variables and analytic spaces (32-XX) 11 Associative rings and algebras (16-XX) 11 Information and communication theory, circuits (94-XX) 10 Computer science (68-XX) 9 Algebraic topology (55-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 General topology (54-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 7 Geometry (51-XX) 7 Statistical mechanics, structure of matter (82-XX) 6 Functions of a complex variable (30-XX) 5 Group theory and generalizations (20-XX) 5 Convex and discrete geometry (52-XX) 4 Category theory; homological algebra (18-XX) 4 Statistics (62-XX) 3 Number theory (11-XX) 3 Potential theory (31-XX) 3 Special functions (33-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Optics, electromagnetic theory (78-XX) 3 Relativity and gravitational theory (83-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Commutative algebra (13-XX) 2 Difference and functional equations (39-XX) 2 Integral equations (45-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Integral transforms, operational calculus (44-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Geophysics (86-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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