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arXiv · 1209.5596

Entropy of homeomorphisms on unimodal inverse limit spaces

Henk Bruin·Sonja Stimac
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Abstract

We prove that every self-homeomorphism $h : K_s \to K_s$ on the inverse limit space $K_s$ of the tent map $T_s$ with slope $s \in (\sqrt 2, 2]$ has topological entropy $\htop(h) = |R| \log s$, where $R \in \Z$ is such that $h$ and $σ^R$ are isotopic. Conclusions on the possible values of the entropy of homeomorphisms of the inverse limit space of a (renormalizable) quadratic map are drawn as well.

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Henk Bruin, Sonja Stimac. 2017-07-10. Entropy of homeomorphisms on unimodal inverse limit spaces. https://doi.org/10.1088/0951-7715%2F26%2F4%2F991

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