On dynamic properties of diffeomorphisms with homoclinic tangency

S. V. Gonchenko; D. V. Turaev; L. P. Shil'nikov

doi:10.1007/pl00021965

On dynamic properties of diffeomorphisms with homoclinic tangency

S. V. Gonchenko
, D. V. Turaev
, L. P. Shil'nikov

Department of Mathematics

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

16 Scopus citations

Abstract

We study dynamic properties of systems in Newhouse domains near a diffeomorphism having a saddle fixed point with a homoclinic tangency in the following cases: one-dimensional, two-dimensional, where a fixed point is a saddle-focus with one real and two complex-conjugate multipliers, and four-dimensional saddle-focus with two pairs of complex-conjugate multipliers.

Original language	English
Pages (from-to)	1317-1343
Number of pages	27
Journal	Journal of Mathematical Sciences
Volume	126
Issue number	4
DOIs	https://doi.org/10.1007/pl00021965
State	Published - 1 Jan 2005

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Applied Mathematics

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10.1007/pl00021965

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title = "On dynamic properties of diffeomorphisms with homoclinic tangency",

abstract = "We study dynamic properties of systems in Newhouse domains near a diffeomorphism having a saddle fixed point with a homoclinic tangency in the following cases: one-dimensional, two-dimensional, where a fixed point is a saddle-focus with one real and two complex-conjugate multipliers, and four-dimensional saddle-focus with two pairs of complex-conjugate multipliers.",

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AU - Gonchenko, S. V.

AU - Turaev, D. V.

AU - Shil'nikov, L. P.

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Y1 - 2005/1/1

N2 - We study dynamic properties of systems in Newhouse domains near a diffeomorphism having a saddle fixed point with a homoclinic tangency in the following cases: one-dimensional, two-dimensional, where a fixed point is a saddle-focus with one real and two complex-conjugate multipliers, and four-dimensional saddle-focus with two pairs of complex-conjugate multipliers.

AB - We study dynamic properties of systems in Newhouse domains near a diffeomorphism having a saddle fixed point with a homoclinic tangency in the following cases: one-dimensional, two-dimensional, where a fixed point is a saddle-focus with one real and two complex-conjugate multipliers, and four-dimensional saddle-focus with two pairs of complex-conjugate multipliers.

UR - https://www.scopus.com/pages/publications/17644427641

U2 - 10.1007/pl00021965

DO - 10.1007/pl00021965

M3 - Article

AN - SCOPUS:17644427641

SN - 1072-3374

VL - 126

SP - 1317

EP - 1343

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

IS - 4

ER -

On dynamic properties of diffeomorphisms with homoclinic tangency

Abstract

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