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arXiv · 2211.10296

Strange attractors for the family of orientation preserving Lozi maps

Przemysław Kucharski
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Abstract

We extend the result of Michal Misiurewicz assuring the existence of strange attractors for the parametrized family $\{f_{(a,b)}\}$ of orientation reversing Lozi maps to the orientation preserving case. That is, we rigorously determine an open subset of the parameter space for which an attractor $\mathcal{A}_{(a,b)}$ of $f_{(a,b)}$ always exists and exhibits chaotic properties. Moreover, we prove that the attractor is maximal in some open parameter region, and arises as the closure of the unstable manifold of a fixed point, on which $f_{(a,b)}|_{\mathcal{A}_{(a,b)}}$ is mixing. We also show that $\mathcal{A}_{(a,b)}$ vary continuously with parameter $(a,b)$ in the Hausdorff metric.

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Przemysław Kucharski. 2022-11-18. Strange attractors for the family of orientation preserving Lozi maps. https://arxiv.org/abs/2211.10296

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