Suzanne Hruska (SUNY Stony Brook)

Constructing Hyperbolic Structures for Hénon maps

Abstract. We will describe a computer algorithm designed to prove hyperbolicity for polynomial diffeomorphisms of ${\ensuremath{\mathbb{R} } }^2$ or ${\ensuremath{\mathbb{C} } }^2$; in particular, for Hénon maps. We will give the classes of Hénon maps for which the computer-assisted proof has been successful, and discuss the numerical and dynamical obstructions found in attempting to prove hyperbolicity for certain other classes of maps.