Saddle hyperbolicity implies hyperbolicity for polynomial automorphisms of $\mathbb{C}^2$

We prove that for a polynomial diffeomorphism of $\mathbb{C}^2$, uniform hyperbolicity on the set of saddle periodic points implies that saddle points are dense in the Julia set. In particular $f$ satisfies Smale’s Axiom A on $\mathbb{C}^2$.

Full Text (PDF format)

This research was partially supported by ANR project LAMBDA, ANR-13-BS01-0002 and a grant from the Institut Universitaire de France.

Received 26 September 2018

Accepted 3 April 2019

Published 20 August 2020