Speaker
Description
In two dimensional unfoldings of homoclinic tangencies, the parameter space contains codimension one laminations whose leaves consist of maps with invariant non hyperbolic Cantor sets. I will describe the geometry and dynamics of these Cantor sets. They are wild both in the senses of Hofbauer–Keller and Newhouse, yet contain Collet–Eckmann points with dense orbits. As a consequence, wildness and non uniform chaotic hyperbolicity coexist on a single invariant set and persist along codimension one parameter families.
Furthermore, each leaf of the lamination also contains maps with infinitely many sinks accumulating on the Cantor set containing the Collet–Eckmann point. The construction is based on a generalized renormalization scheme for two dimensional systems, which will be outlined in the talk.