Existence of generic cubic homoclinic tangencies for H\'enon maps

Shin Kiriki; Teruhiko Soma

Existence of generic cubic homoclinic tangencies for H\'enon maps

Dynamical Systems 2012-03-20 v3

Authors: Shin Kiriki , Teruhiko Soma

Abstract

In this paper, we show that the H\'enon map $\varphi_{a,b}$ has a generically unfolding cubic tangency for some $(a,b)$ arbitrarily close to $(-2,0)$ by applying results of Gonchenko-Shilnikov-Turaev [12]-[16]. Combining this fact with theorems in Kiriki-Soma [20], one can observe the new phenomena in the H\'enon family, appearance of persistent antimonotonic tangencies and cubic polynomial-like strange attractors.

Keywords

hénon maps cubic homoclinic tangencies generic unfolding strange attractors dynamical systems

Cite

@article{arxiv.math/0608386,
  title  = {Existence of generic cubic homoclinic tangencies for H\'enon maps},
  author = {Shin Kiriki and Teruhiko Soma},
  journal= {arXiv preprint arXiv:math/0608386},
  year   = {2012}
}

Comments

accepted in Ergod. Th. & Dynam. Sys. 16 Feb 2012

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