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Found 356 Documents (Results 1–100)

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Non-integrability of the Kepler and the two-body problems on the Heisenberg group. (English) Zbl 07413747

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Arnold diffusion for smooth systems of two and a half degrees of freedom. (English) Zbl 1466.37001

Annals of Mathematics Studies 208. Princeton, NJ: Princeton University Press (ISBN 978-0-691-20253-2/hbk; 978-0-691-20252-5/pbk; 978-0-691-20493-2/ebook). xiii, 204 p. (2020).
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Topological obstacles to the realizability of integrable Hamiltonian systems by billiards. (English. Russian original) Zbl 1439.37056

Dokl. Math. 100, No. 2, 463-466 (2019); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 488, No. 5, 471-475 (2019).
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Polynomial non-integrability of magnetic billiards on the sphere and the hyperbolic plane. (English. Russian original) Zbl 1439.37054

Russ. Math. Surv. 74, No. 2, 187-209 (2019); translation from Usp. Mat. Nauk 74, No. 2, 3-26 (2019).
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Topological integrability, classical and quantum chaos, and the theory of dynamical systems in the physics of condensed matter. (English. Russian original) Zbl 1439.37062

Russ. Math. Surv. 74, No. 1, 141-173 (2019); translation from Usp. Mat. Nauk 74, No. 1, 149-184 (2019).
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Liouville integrability of sub-Riemannian problems on Carnot groups of step 4 or greater. (English. Russian original) Zbl 1394.37091

Sb. Math. 209, No. 5, 672-713 (2018); translation from Mat. Sb. 209, No. 5, 74-119 (2018).
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Topology, singularities and integrability in Hamiltonian systems with two degrees of freedom. (English. Russian original) Zbl 1378.37096

Izv. Math. 81, No. 4, 671-687 (2017); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 81, No. 4, 3-19 (2017).
MSC:  37J30 70H05 34C40 37J05 37J35
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Nonlinear dynamics. Non-integrable systems and chaotic dynamics. (English) Zbl 1358.37098

De Gruyter Studies in Mathematical Physics 36. Berlin: De Gruyter (ISBN 978-3-11-043938-0/hbk; 978-3-11-043058-5/ebook). xiv, 283 p. (2017).
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Analysis of a constrained two-body problem. (English) Zbl 1397.70029

Awrejcewicz, Jan (ed.), Dynamical systems: theoretical and experimental analysis, Łódź, Poland, December 7–10, 2015. Proceedings. Cham: Springer (ISBN 978-3-319-42407-1/hbk; 978-3-319-42408-8/ebook). Springer Proceedings in Mathematics & Statistics 182, 361-372 (2016).
MSC:  70H45 70F05 37J30
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Representation of solutions to the problem of the motion of a heavy rigid body in the Kovalevskaya case in terms of Weierstrass \(\zeta\)- and \(\wp\)-functions and nonintegrability of the Hess case by quadratures. (English. Russian original) Zbl 1401.70007

Sb. Math. 207, No. 7, 889-914 (2016); translation from Mat. Sb. 207, No. 7, 3-28 (2016).
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Integrable systems and differential Galois theory. (English) Zbl 1418.37096

Bolsinov, Alexey et al., Geometry and dynamics of integrable systems. Lecture notes for the advanced course, Barcelona, Spain, September 2013. Edited by Eva Miranda and Vladimir Matveev. Basel: Birkhäuser/Springer. Adv. Courses in Math., CRM Barcelona, 1-33 (2016).
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Degenerate resonances in Hamiltonian systems: from Poincaré-Birkhoff chains to vortex pairs and Kármán vortex streets. (English. Russian original) Zbl 1353.37123

J. Math. Sci., New York 219, No. 1, 155-159 (2016); translation from Probl. Mat. Anal. 85, 147-151 (2016).
MSC:  37J40 37J30 70H08
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Integrable cases in the dynamics of a multi-dimensional rigid body in a nonconservative field in the presence of a tracking force. (English. Russian original) Zbl 1353.70021

J. Math. Sci., New York 214, No. 6, 865-891 (2016); translation from Fundam. Prikl. Mat. 19, No. 3, 187-222 (2014).
MSC:  70E40 37J30
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The splitting of separatrices, the branching of solutions, and nonintegrability of many-dimensional systems. application to the problem of the motion of a spherical pendulum with an oscillating suspension point. (English. Russian original) Zbl 1426.37048

J. Math. Sci., New York 214, No. 6, 755-801 (2016); translation from Fundam. Prikl. Mat. 19, No. 3, 23-90 (2014).
MSC:  37J30 37J10 70E17
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Homogeneous systems with quadratic integrals, Lie-Poisson quasibrackets, and Kovalevskaya’s method. (English) Zbl 1358.37099

Sb. Math. 206, No. 12, 1682-1706 (2015); translation from Mat. Sb. 206, No. 12, 29-54 (2015).
MSC:  37J35 37J05 37J30 70E45 70H05 70H06 70H07
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