The Pruning Front Conjecture and Classification of Hénon Maps with Strange Attractors

Explore a lecture on the topological dynamics of Hénon maps, focusing on recent results obtained in collaboration with Jan Boroński. Delve into the pruning front conjecture, kneading theory, and a classification of Hénon maps in the presence of strange attractors. Examine the generalization of Benedicks-Carleson parameters through the Wang-Young parameter set. Discover how two Hénon maps can be conjugate on their strange attractors, and learn about the conditions for this conjugacy based on kneading sequences and folding patterns. Gain insights into the inverse limit description of Hénon attractors using densely branching trees, which forms the foundation for the classification results presented in this talk.