Existence of generic cubic homoclinic tangencies for Hénon maps

2006/08/15 by Kiriki, Shin, Soma, Teruhiko
#37D20 #37D25 #37D45 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0608386

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.

Related

• Bifurcations of cubic homoclinic tangencies in two-dimensional\n symplectic maps
• The pruning front conjecture, folding patterns and classification of Hénon maps in the presence of strange attractors
• Newhouse Laminations
• Homoclinic tangencies to resonant saddles and discrete Lorenz attractors
• Degenerate homoclinic bifurcations in complex dimension 2