On the Structure of Lorenz Maps

Paulo Brandão

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arXiv · 1402.2862

On the Structure of Lorenz Maps

Paulo Brandão

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Abstract

We study the non-wandering set of $C^3$ contracting Lorenz maps $f$ with negative Schwarzian derivative. We show that if $f$ doesn't have attracting periodic orbit, then there is a unique topological attractor. Precisely, there is a transitive compact set $\Lambda$ such that $\omega_f(x)=\Lambda$ for a residual set of points $x \in [0,1]$. We also develop in the context of Lorenz maps the classical theory of spectral decomposition constructed for Axiom A maps by Smale.

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Paulo Brandão. 2014-02-12. On the Structure of Lorenz Maps. https://arxiv.org/abs/1402.2862

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