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arXiv · 1207.2872

The topological complexity of Cantor attractors for unimodal interval maps

Simin Li·Weixiao Shen
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Abstract

For a non-flat $C^3$ unimodal map with a Cantor attractor, we show that for any open cover $\mathcal U$ of this attractor, the complexity function $p(\mathcal U, n)$ is of order $n\log n$. In the appendix, we construct a non-renormalizable map with a Cantor attractor for which $p(\mathcal{U}, n)$ is bounded from above for any open cover $\mathcal{U}$.

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Simin Li, Weixiao Shen. 2013-12-03. The topological complexity of Cantor attractors for unimodal interval maps. https://arxiv.org/abs/1207.2872

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