Dynamics near nonhyperbolic fixed points or nontransverse homoclinic points

We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodic points are obtained. A new method, based on the study of the dynamics of center disks, is introduced.

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Bibliographic Details
Published in:Mathematics and computers in simulation 2014-01, Vol.95, p.163-179
Main Author: Kryzhevich, Sergey
Format: Article
Language:English
Subjects:
Center unstable manifold
Chaos
Homoclinic point
Partial hyperbolicity
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Description
Summary:We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodic points are obtained. A new method, based on the study of the dynamics of center disks, is introduced.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2012.07.007