Existence and genericity problems for dynamical systems with nonzero Lyapunov exponents

Ya Pesin

doi:10.1134/S1560354707050024

Existence and genericity problems for dynamical systems with nonzero Lyapunov exponents

Ya Pesin

Research output: Contribution to journal › Review article › peer-review

10 Scopus citations

Abstract

This is a survey-type article whose goal is to review some recent results on existence of hyperbolic dynamical systems with discrete time on compact smooth manifolds and on coexistence of hyperbolic and non-hyperbolic behavior. It also discusses two approaches to the study of genericity of systems with nonzero Lyapunov exponents.

Original language	English (US)
Pages (from-to)	476-489
Number of pages	14
Journal	Regular and Chaotic Dynamics
Volume	12
Issue number	5
DOIs	https://doi.org/10.1134/S1560354707050024
State	Published - 2007

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

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10.1134/S1560354707050024

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title = "Existence and genericity problems for dynamical systems with nonzero Lyapunov exponents",

abstract = "This is a survey-type article whose goal is to review some recent results on existence of hyperbolic dynamical systems with discrete time on compact smooth manifolds and on coexistence of hyperbolic and non-hyperbolic behavior. It also discusses two approaches to the study of genericity of systems with nonzero Lyapunov exponents.",

author = "Ya Pesin",

note = "Funding Information: ACKNOWLEDGMENTS Ya. P. is partially supported by NSF grant DMS-0503810.",

year = "2007",

doi = "10.1134/S1560354707050024",

language = "English (US)",

volume = "12",

pages = "476--489",

journal = "Regular and Chaotic Dynamics",

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T1 - Existence and genericity problems for dynamical systems with nonzero Lyapunov exponents

AU - Pesin, Ya

N1 - Funding Information: ACKNOWLEDGMENTS Ya. P. is partially supported by NSF grant DMS-0503810.

PY - 2007

Y1 - 2007

N2 - This is a survey-type article whose goal is to review some recent results on existence of hyperbolic dynamical systems with discrete time on compact smooth manifolds and on coexistence of hyperbolic and non-hyperbolic behavior. It also discusses two approaches to the study of genericity of systems with nonzero Lyapunov exponents.

AB - This is a survey-type article whose goal is to review some recent results on existence of hyperbolic dynamical systems with discrete time on compact smooth manifolds and on coexistence of hyperbolic and non-hyperbolic behavior. It also discusses two approaches to the study of genericity of systems with nonzero Lyapunov exponents.

UR - https://www.scopus.com/pages/publications/77953312559

UR - https://www.scopus.com/pages/publications/77953312559#tab=citedBy

U2 - 10.1134/S1560354707050024

DO - 10.1134/S1560354707050024

M3 - Review article

AN - SCOPUS:77953312559

SN - 1560-3547

VL - 12

SP - 476

EP - 489

JO - Regular and Chaotic Dynamics

JF - Regular and Chaotic Dynamics

IS - 5

ER -

Existence and genericity problems for dynamical systems with nonzero Lyapunov exponents

Abstract

All Science Journal Classification (ASJC) codes

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