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arXiv · 1903.10183

Entropy in uniformly quasiregular dynamics

Ilmari Kangasniemi·Yûsuke Okuyama·Pekka Pankka·Tuomas Sahlsten
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Abstract

Let $M$ be a closed, oriented, and connected Riemannian $n$-manifold, for $n\ge 2$, which is not a rational homology sphere. We show that, for a non-constant and non-injective uniformly quasiregular self-map $f\colon M\to M$, the topological entropy $h(f)$ is $\log \mathrm{deg}( f )$. This proves Shub's entropy conjecture in this case.

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Ilmari Kangasniemi, Yûsuke Okuyama, Pekka Pankka, Tuomas Sahlsten. 2019-03-25. Entropy in uniformly quasiregular dynamics. https://doi.org/10.1017/etds.2020.51

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