Existence of generic cubic homoclinic tangencies for H\'enon maps
Abstract
In this paper, we show that the H\'enon map 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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