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Entropy in uniformly quasiregular dynamics
Published online by Cambridge University Press: 22 June 2020
Abstract
Let $M$ be a closed, oriented, and connected Riemannian $n$-manifold, for $n\geq 2$, which is not a rational homology sphere. We show that, for a non-constant and non-injective uniformly quasiregular self-map $f:M\rightarrow M$, the topological entropy $h(f)$ is $\log \deg f$. This proves Shub’s entropy conjecture in this case.
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- © The Author(s) 2020. Published by Cambridge University Press
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