Dynamics and computations

Rigidity for complex Hénon maps

The seminar will take place on Zoom

Abstract: The forward escaping set of a dissipative complex Hénon map is a well-understood dynamical object. By works of Hubbard & Oberste-Vorth it is biholomorphic to an universal object: (C-\bar{D})xC factored by a discrete group of automorphisms isomorphic to Z[1/2]/Z. We use this analytic description to show that two Hénon maps with biholomorphic escaping sets are in fact the same. In her work Tanase extended this description of the escaping set to the boundary in order to capture the Julia set and introduced a one-dimensional invariant set that encodes part of the dynamics of the Hénon map. We show that this invariant is also a rigid object for the Hénon map. This talk is based on joint work with Sylvain Bonnot and Raluca Tanase.