On dynamical properties of multidimensional diffeomorphisms from Newhouse regions: I

S. V. Gonchenko; L. P. Shilnikov; D. V. Turaev

doi:10.1088/0951-7715/21/5/003

On dynamical properties of multidimensional diffeomorphisms from Newhouse regions: I

S. V. Gonchenko, L. P. Shilnikov, D. V. Turaev

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

68 Scopus citations

Abstract

The phenomenon of the generic coexistence of infinitely many periodic orbits with different numbers of positive Lyapunov exponents is analysed. Bifurcations of periodic orbits near a homoclinic tangency are studied. Criteria for the coexistence of infinitely many stable periodic orbits and for the coexistence of infinitely many stable invariant tori are given.

Original language	English
Pages (from-to)	923-972
Number of pages	50
Journal	Nonlinearity
Volume	21
Issue number	5
DOIs	https://doi.org/10.1088/0951-7715/21/5/003
State	Published - 1 May 2008

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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10.1088/0951-7715/21/5/003

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title = "On dynamical properties of multidimensional diffeomorphisms from Newhouse regions: I",

abstract = "The phenomenon of the generic coexistence of infinitely many periodic orbits with different numbers of positive Lyapunov exponents is analysed. Bifurcations of periodic orbits near a homoclinic tangency are studied. Criteria for the coexistence of infinitely many stable periodic orbits and for the coexistence of infinitely many stable invariant tori are given.",

author = "Gonchenko, \{S. V.\} and Shilnikov, \{L. P.\} and Turaev, \{D. V.\}",

year = "2008",

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doi = "10.1088/0951-7715/21/5/003",

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T2 - I

AU - Gonchenko, S. V.

AU - Shilnikov, L. P.

AU - Turaev, D. V.

PY - 2008/5/1

Y1 - 2008/5/1

N2 - The phenomenon of the generic coexistence of infinitely many periodic orbits with different numbers of positive Lyapunov exponents is analysed. Bifurcations of periodic orbits near a homoclinic tangency are studied. Criteria for the coexistence of infinitely many stable periodic orbits and for the coexistence of infinitely many stable invariant tori are given.

AB - The phenomenon of the generic coexistence of infinitely many periodic orbits with different numbers of positive Lyapunov exponents is analysed. Bifurcations of periodic orbits near a homoclinic tangency are studied. Criteria for the coexistence of infinitely many stable periodic orbits and for the coexistence of infinitely many stable invariant tori are given.

UR - https://www.scopus.com/pages/publications/43049144272

U2 - 10.1088/0951-7715/21/5/003

DO - 10.1088/0951-7715/21/5/003

M3 - Article

AN - SCOPUS:43049144272

SN - 0951-7715

VL - 21

SP - 923

EP - 972

JO - Nonlinearity

JF - Nonlinearity

IS - 5

ER -

On dynamical properties of multidimensional diffeomorphisms from Newhouse regions: I

Abstract

ASJC Scopus subject areas

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