Entropy of homeomorphisms on unimodal inverse limit spaces

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 $R\in \mathbb{Z}$ is such that $h$ and ${\sigma }^R$ 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.

References in corpus (1)

• Inverse limits as attractors in parameterized families