Existence of generic cubic homoclinic tangencies for Hénon maps

Details Existence of generic cubic homoclinic tangencies for Hénon maps Existence of generic cubic homoclinic tangencies for Hénon maps

2006-08-15

arxiv.org/abs/math/0608386v3

Mathematics

Dynamical Systems

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

Scientific paper

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.

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