# 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.

References:

[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.