Jan Boronski (Jagiellonian University, Krakow)

Abstract

In my talk I shall present my work with Sonja Štimac on Hénon maps with strange attractors (Wang-Young parameters). First, I shall explain a construction (inspired by a work of Crovisier and Pujals on mildly dissipative diffeomorphisms of the plane) of conjugacy of these maps to the shift homeomorphisms on inverse limits of dendrites with dense set of branch points, and a characterization of orbits of critical points in terms of these inverse limits. Then I will explain how this leads to a classification of conjugacy classes of such maps in terms of a single sequence of 0s and 1s.

References:

Boronski J., Štimac S; Densely branching trees as models for Hénon-like and Lozi-like attractors, Advances in Mathematics 429 (2023) 109191

Boronski J., Štimac S; The pruning front conjecture, folding patterns and classification of Hénon maps in the presence of strange attractors, arXiv:2302.12568v2