Strange attractors and densely branching trees for the generalized Lozi-like family

Przemysław Kucharski

Published 2023-02-09Version 1

We generalize the Lozi-like family introduced in [M\v{S}17]. The generalized Lozi-like family encompasses in particular certain Lozi-like maps [M\v{S}17], orientation preserving or reversing Lozi maps or large parameter regions of 2-dimensional border collision normal forms [GS21]. We prove that it possesses a strange attractor, arising as a homoclinic class. We apply obtained results to extend the Misiurewicz set [Mis80] and its generalization to the orientation preserving case [Kuc22]. We also strengthen results of Paul Glendinning and David Simpson regarding existence of strange attractors for 2-dimensional border collision normal forms [GS22a, GS21]. We also build a model as an inverse limit of densely branching trees for mentioned families, extending results of Jan Boro\'nski and Sonja \v{S}timac from [Bor21].