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Dynamical Systems with Nontrivially Recurrent Invariant Manifolds

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Dynamics, Games and Science I

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 1))

Abstract

The goal of this article to give exposition of results demonstrating deep interrelation between topological classification of Dynamical Systems with nontrivially recurrent invariant manifolds and topological classification of standard objects existing on ambient manifold. One can see how the purely topological constructions, very pathological at first glance, appear naturally in Dynamical Systems.

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Acknowledgements

The research was partially supported by RFFI grant 08-01-00547. The authors are grateful to D. Anosov, V. Medvedev, and R. Plykin for useful discussions.

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Authors and Affiliations

  1. Nizhny Novgorod State University, 23 Gagarin Ave, Nizhny Novgorod, 603950, Russia

    Viacheslav Grines

  2. Nizhny Novgorod State Pedagogical University, 1 Ulyanova Str., Nizhny Novgorod, 603600, Russia

    Evgeny Zhuzhoma

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  1. Viacheslav Grines
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  2. Evgeny Zhuzhoma
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Correspondence to Viacheslav Grines .

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    Mauricio Matos Peixoto

  2. Faculdade de Ciências, Departamento de Matemática, Universidade do Porto, Rua do Campo Alegre 687, Porto, 4169-007, Portugal

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  3. Warwick Systems Biology, University of Warwick, Coventry House, Coventry, CV4 7AL, United Kingdom

    David A. Rand

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Grines, V., Zhuzhoma, E. (2011). Dynamical Systems with Nontrivially Recurrent Invariant Manifolds. In: Peixoto, M., Pinto, A., Rand, D. (eds) Dynamics, Games and Science I. Springer Proceedings in Mathematics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11456-4_29

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