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arXiv · 1612.00093

Topological Attractors of Contracting Lorenz Maps

Paulo Brandão
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Abstract

We study the non-wandering set of contracting Lorenz maps. We show that if such a map $f$ doesn't have any attracting periodic orbit, then there is a unique topological attractor. Precisely, there is a compact set $\Lambda$ such that $\omega_f(x)=\Lambda$ for a residual set of points $x \in [0,1]$. Furthermore, we classify the possible kinds of attractors that may occur.

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Paulo Brandão. 2016-12-01. Topological Attractors of Contracting Lorenz Maps. https://arxiv.org/abs/1612.00093

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