Liviana Palmisano: Coexistence of attractors

One of the aims of dynamics is to understand the long term behavior of orbits. This involves the study of the attractors of the system. We focus on the attractors for Hénon maps and we prove the coexistence of multiple attractors. There are Hénon maps which exhibit simultaneously finitely many periodic attractors and a strange attractor. Moreover the Newhouse phenomena holds in the Hénon family, i.e. there are maps with infinitely many periodic attractors, sinks with arbitrarily large period.

Furthermore, we prove that the Newhouse phenomena also holds for general families of high dimensional maps which unfold a homoclinic tangency and that it is stable. More in details, in every unfolding there is a set of maps with infinitely many sinks which form a codimension two lamination. The sinks move smoothly, creating a lamination.