On models with non-rough Poincaré homoclinic curves

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

doi:10.1016/0167-2789(93)90268-6

On models with non-rough Poincaré homoclinic curves

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

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

92 Scopus citations

Abstract

The possibility of an a priori complete description of finite-parameter models including systems with structurally unstable Poincaré homoclinic curves is studied. The main result reported here is that systems having a countable set of moduli of ω-equivalence and systems having infinitely many degenerate periodic and homoclinic orbits are dense in the Newhouse regions of ω-non-stability. We discuss the question of correctly setting a problem for the analysis of models of such type.

Original language	English
Pages (from-to)	1-14
Number of pages	14
Journal	Physica D: Nonlinear Phenomena
Volume	62
Issue number	1-4
DOIs	https://doi.org/10.1016/0167-2789(93)90268-6
State	Published - 30 Jan 1993
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/0167-2789(93)90268-6

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abstract = "The possibility of an a priori complete description of finite-parameter models including systems with structurally unstable Poincar{\'e} homoclinic curves is studied. The main result reported here is that systems having a countable set of moduli of ω-equivalence and systems having infinitely many degenerate periodic and homoclinic orbits are dense in the Newhouse regions of ω-non-stability. We discuss the question of correctly setting a problem for the analysis of models of such type.",

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AU - Turaev, D. V.

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AB - The possibility of an a priori complete description of finite-parameter models including systems with structurally unstable Poincaré homoclinic curves is studied. The main result reported here is that systems having a countable set of moduli of ω-equivalence and systems having infinitely many degenerate periodic and homoclinic orbits are dense in the Newhouse regions of ω-non-stability. We discuss the question of correctly setting a problem for the analysis of models of such type.

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On models with non-rough Poincaré homoclinic curves

Abstract

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