Abstract
AbstractLet$M$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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