Persistent homoclinic tangencies and infinitely many sinks for residual sets of automorphisms of low degree in C^{3}

Abstract

We show that there exists a polynomial automorphism $f$ of ${\mathbb{C}}^3$ of degree 2 such that for every automorphism $g$ sufficiently close to $f$, $g$ admits a tangency between the stable and unstable laminations of some hyperbolic set. As a consequence, for each $d\ge 2$, there exists an open set of polynomial automorphisms of degree at most $d$ in which the automorphisms having infinitely many sinks are dense. To prove these results, we give a complex analogous to the notion of blender introduced by Bonatti and Diaz.

References in corpus (2)

• Non density of stability for holomorphic mappings on P^k
• Robust tangencies of large codimension

Cited by in corpus (2)

• Newhouse Laminations
• Newhouse Laminations of polynomials on ${\mathbb{C}}^2$