V. V. Kozlov, “Dynamical Systems with Multivalued Integrals on a Torus”, Dynamical systems and optimization, Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov, Trudy Mat. Inst. Steklova, 256, Nauka, MAIK «Nauka/Inteperiodika», M., 2007, 201–218; Proc. Steklov Inst. Math., 256 (2007), 188

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Volume 256, Pages 201–218 (Mi tm462)

This article is cited in 21 scientific papers (total in 21 papers)

Dynamical Systems with Multivalued Integrals on a Torus

V. V. Kozlov

Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (236 kB) Citations (21)

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Abstract: Properties of the solutions to differential equations on the torus with a complete set of multivalued first integrals are considered, including the existence of an invariant measure, the averaging principle, and the infiniteness of the number of zeros for integrals of zero-mean functions along trajectories. The behavior of systems with closed trajectories of large period is studied. It is shown that a generic system acquires a limit mixing property as the periods tend to infinity.

Received in August 2006

English version:
Proceedings of the Steklov Institute of Mathematics, 2007, Volume 256, Pages 188–205
DOI: https://doi.org/10.1134/S0081543807010105

Bibliographic databases:

Document Type: Article

UDC: 519.21

Language: Russian

Citation: V. V. Kozlov, “Dynamical Systems with Multivalued Integrals on a Torus”, Dynamical systems and optimization, Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov, Trudy Mat. Inst. Steklova, 256, Nauka, MAIK «Nauka/Inteperiodika», M., 2007, 201–218; Proc. Steklov Inst. Math., 256 (2007), 188–205

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tm462

https://www.mathnet.ru/eng/tm/v256/p201

This publication is cited in the following 21 articles:

N. V. Denisova, “Recurrence of integrals of conditionally periodic functions”, Dokl. Math., 108:1 (2023), 316–319
Yuchen He, Hongkai Zhao, Yimin Zhong, “How Much Can One Learn a Partial Differential Equation from Its Solution?”, Found Comput Math, 2023
V. V. Kozlov, “On the integrability of the equations of dynamics in a non-potential force field”, Russian Math. Surveys, 77:6 (2022), 1087–1106
N. V. Denisova, “On the dynamics of systems with two degrees of freedom”, Dokl. Math., 105:1 (2022), 1–5
Kozlov V.V., “On the Problem of Separation of Variables in Systems of Ordinary Differential Equations”, Differ. Equ., 57:10 (2021), 1299–1306
V. V. Kozlov, “Tensor invariants and integration of differential equations”, Russian Math. Surveys, 74:1 (2019), 111–140
De Leo R., “A Survey on Quasiperiodic Topology”, Advanced Mathematical Methods in Biosciences and Applications, Steam-H Science Technology Engineering Agriculture Mathematics & Health, ed. Berezovskaya F. Toni B., Springer International Publishing Ag, 2019, 53–88
Karakhanyan A.L., Shahgholian H., “On a Conjecture of de Giorgi Related to Homogenization”, Ann. Mat. Pura Appl., 196:6 (2017), 2167–2183
Kozlov V.V., “On the equations of the hydrodynamic type”, Pmm-J. Appl. Math. Mech., 80:3 (2016), 209–214
V. I. Dragović, M. Radnović, “Pseudo-integrable billiards and double reflection nets”, Russian Math. Surveys, 70:1 (2015), 1–31
I. A. Bizyaev, V. V. Kozlov, “Homogeneous systems with quadratic integrals, Lie-Poisson quasibrackets, and Kovalevskaya's method”, Sb. Math., 206:12 (2015), 1682–1706
A. Yu. Anikin, J. Brüning, S. Yu. Dobrokhotov, “Averaging and trajectories of a Hamiltonian system appearing in graphene placed in a strong magnetic field and a periodic potential”, J. Math. Sci., 223:6 (2017), 656–666
V. V. Kozlov, “Dinamika sistem s servosvyazyami. II”, Nelineinaya dinam., 11:3 (2015), 579–611
Valery V. Kozlov, “The Dynamics of Systems with Servoconstraints. II”, Regul. Chaotic Dyn., 20:4 (2015), 401–427
V. V. Kozlov, “Liouville's equation as a Schrödinger equation”, Izv. Math., 78:4 (2014), 744–757
Bizyaev I.A., “Nonintegrability and Obstructions To the Hamiltonianization of a Nonholonomic Chaplygin TOP”, Dokl. Math., 90:2 (2014), 631–634
Dragovic V., Radnovic M., “Pseudo-Integrable Billiards and Arithmetic Dynamics”, J. Mod. Dyn., 8:1 (2014), 109–132
V. V. Kozlov, “On Bohl's Argument Theorem”, Math. Notes, 93:1 (2013), 83–89
A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Problema dreifa i vozvraschaemosti pri kachenii shara Chaplygina”, Nelineinaya dinam., 9:4 (2013), 721–754
Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “The Problem of Drift and Recurrence for the Rolling Chaplygin Ball”, Regul. Chaotic Dyn., 18:6 (2013), 832–859

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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