Jan P. Boronski: The pruning front conjecture and a classification of Hénon maps
Time: Thu 2022-12-01 13.00
Location: Room 3418, Lindstedtsvägen 25
Participating: Jan P. Boronski (AGH University of Science and Technology)
Abstract: I will present my joint work with Sonja Štimac in which we classify Hénon maps within Benedicks-Carleson parameter set. Besides the paper of Benedicks and Carleson [BC], our work relies on two components. The first is the notion of mild dissipation [CP], which allows for an inverse limit description, in terms of densely branching trees [BS]. The second is the introduction of a kneading theory for these maps, as well as folding patterns, similar to the case of Lozi maps [MS] (see also [BBS]).
Two Hénon maps from Benedicks-Carleson family are conjugate on their strange attractors if and only if their kneading sequences coincide, if and only if their folding patterns agree.
[BBS] M. Barge, H. Bruin, S. Štimac, The Ingram conjecture. Geom. Topol. 16 (2012), no. 4, 2481–2516.
[BC] M. Benedicks, L.A.E. Carleson, The dynamics of the Henon map, Annals of Mathematics 133 (1991), 73–169.
[BS] J. Boroński, S. Štimac, Densely branching trees as models for Henon-like and Lozi-like attractors, preprint 2021, arXiv:2104.14780
[CP] S. Crovisier, E. Pujals, Strongly dissipative surface diffeomorphisms, Commentarii Mathematici Helvetici 93 (2018), 377–400.
[MS] M. Misiurewicz, S. Štimac, Symbolic dynamics for Lozi maps, Nonlinearity 29 (2016), 3031–3046.