Lorenzo Guerini, a student of one of the members of the CAS research group Several Complex Variables and Complex Dynamics will give the talk titled "The Julia Set of hyperbolic Hénon maps" at CAS Oslo Thursday April 27.

Abstract

It is well known that the Julia set of a rational map coincides with the closure of the set of its repelling periodic points.

Given an Hénon map f one can reasonably hope that J, the Julia set of f, coincides with J*, the closure of the saddle periodic points.

In 1991 Bedford and Smillie proved that the sets J and J* coincide when f acts uniformly hyperbolically on J.

In 2006 Fornæss claimed equality under the weaker assumption that f acts uniformly hyperbolically on the potentially smaller set J*. Unfortunately his proof is not complete.

In this talk we complete the proof using the additional assumption of substantial dissipativity. It turns out that the proof works under slightly weaker hyperbolicity assumptions, which we will discuss if time permits.