Extensive research has previously been carried out on the existence of strange attractors in
2D piecewise linear maps, including the renowned Lozi map. However, the rigorous …

Hénon Maps: A List of Open Problems | Arnold Mathematical Journal Skip to main content
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We extend the result of Michał Misiurewicz assuring the existence of strange attractors for
the parametrized family {f (a, b)} of orientation reversing Lozi maps to the orientation …

Inspired by a recent work of Crovisier and Pujals on mildly dissipative diffeomorphisms of
the plane, we show that Hénon-like and Lozi-like maps on their strange attractors are …

The border-collision normal form describes the local dynamics in continuous systems with
switches when a fixed point intersects a switching surface. For one-dimensional cases …

We introduce a renormalization model which explains how the behavior of a discrete-time
continuous dynamical system changes as the dimension of the system varies. The model …

We study the topological dynamics of H\'enon maps. For a parameter set generalizing the
Benedicks-Carleson parameters (the Wang-Young parameter set) we obtain the following …

Since its original publication in 1978, Lozi's chaotic map has been thoroughly explored and
continues to be. Hundreds of publications have analyzed its particular structure or applied its …

arXiv:2312.03907v1 [math.DS] 6 Dec 2023 Page 1 HENON MAPS: A LIST OF OPEN
PROBLEMS by Julia Xénelkis de Hénon Abstract. — We propose a set of questions on the …

In this paper, we give a mathematical proof to the existence of a strange attractor for the Lozi
mapping L. More precisely, we prove that L has a unique strange attractor for the parameter …