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Existence of generic cubic homoclinic tangencies for Hénon maps

Shin Kiriki·Teruhiko Soma
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Abstract

In this paper, we show that the Hénon map $φ_{a,b}$ 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 Hénon family, appearance of persistent antimonotonic tangencies and cubic polynomial-like strange attractors.

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Shin Kiriki, Teruhiko Soma. 2012-03-19. Existence of generic cubic homoclinic tangencies for Hénon maps. https://arxiv.org/abs/math/0608386

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