The topological complexity of Cantor attractors for unimodal interval maps

Li, Simin; Shen, Weixiao

doi:10.1090/S0002-9947-2015-06372-7

The topological complexity of Cantor attractors for unimodal interval maps
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by Simin Li and Weixiao Shen PDF

Trans. Amer. Math. Soc. 368 (2016), 659-688 Request permission

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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