Sonja Štimac (University of Zagreb) скачать в хорошем качестве

Sonja Štimac (University of Zagreb)

Title: The pruning front conjecture and a classification of Hénon maps in the presence of strange attractors Abstract: I will talk about recent results on topological dynamics of Hénon maps obtained in joint work with Jan Boroński. For a parameter set generalizing the Benedicks-Carleson parameters (the Wang-Young parameter set) we obtain the following: The pruning front conjecture (due to Cvitanovi¢, Gunaratne, and Procacci); A kneading theory (realizing a conjecture by Benedicks and Carleson); A classification: two Hénon maps are conjugate on their strange attractors if and only if their sets of kneading sequences coincide, if and only if their folding patterns coincide. The classification result relies on a further development of the authors' recent inverse limit description of Hénon attractors in terms of densely branching trees. (Joint work with Jan P. Boroński)