Mikhail Lyubich, Stony Brook University
Feigenbaum Henon maps are infinitely renormalizable quadratic automorphisms of the real or complex 2D spaces. Over the past 20 years a rich theory of strongly dissipative maps of this class has been developed. It includes Universality and (non-)Rigidity phenomena, description of an intricate heteroclinic web, and construction of wild attractors and Julia sets of positive measure. Some of these features are similar to their 1D counterparts but some are strikingly different. In the talk we will give an overview of this theory. If time permits, we will mention the current work in progress on the axiomatic non-perturbative theory of “unimodal Henon maps” based upon quantitative Pesin theory.
Based upon joint work with Artur Avila, Marco Martens, and many other people.