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arXiv · 1912.09548

Stable intersections of Cantor sets and positive density of persistent tangencies for homoclinic bifurcations of automorphisms of $\mathbb{C}^2$

Hugo Araújo·Carlos Gustavo Moreira
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Abstract

Let $\{f_\mu\}_{\mu \in \mathbb{D}}$ be a family of automorphisms of $\mathbb{C}^2$ unfolding a generic homoclinic tangency associated to a fixed point $p$ belonging to a horseshoe. We prove that if the linearized versions of the Cantor sets representing the local intersections of the stable and unstable manifolds of $p$ with the horseshoe have stable intersections, then the set of parameters $\mu$ corresponding to automorphisms with persistent tangencies has positive density at $\mu = 0$.

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Hugo Araújo, Carlos Gustavo Moreira. 2019-12-19. Stable intersections of Cantor sets and positive density of persistent tangencies for homoclinic bifurcations of automorphisms of $\mathbb{C}^2$. https://arxiv.org/abs/1912.09548

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