Strange attractors for the family of orientation preserving Lozi maps

What is it about?

The article is devoted to the study of strange attractors, nowadays one of the principal objects in the theory of dynamical systems. An strange attractor is a set of states, that the system is expected to approach with the progress of time for a considerable amount of initial conditions. Strange attractors arise naturally in many different contexts, such as physical electronic chaotic circuits, models for atmospheric convection, or chemical reactions. In this article we show the existence of strange attractors for certain class of transformations of the plane.

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Photo by Visax on Unsplash

Photo by Visax on Unsplash

Why is it important?

Our work shows that the strange attractor approximates well nearby orbits. Moreover, the found attractor is maximal in its neighbourhood. This feature is much harder to obtain in the orientation preserving case of the Lozi family. Possible generalizations include other piecewise affine models and their perturbations exhibiting a certain degree of hyperbolicity.