Stable intersections of Cantor sets and positive density of persistent tangencies for homoclinic bifurcations of automorphisms of ℂ²

2019/12/19 by Hugo Rodrigues Araujo, Araújo, Hugo, Carlos Gustavo Moreira +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1912.09548

openalex publication_date 2019/12/19 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28

Abstract

Let \f_μ\_μ∈ \mathbbD be a family of automorphisms of ℂ² 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 μ corresponding to automorphisms with persistent tangencies has positive density at μ= 0.

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