3 problems

Let $f$ be a $C^r$ surface diffeomorphism, where $1<r<\infty$, let $h_{\operatorname{top}}(f)$ denote its topological entropy, and let…

Let $f$ be a $C^r$ surface diffeomorphism, where $1<r<\infty$, and let $h_{\operatorname{top}}(f)$ be its topological entropy. A measure maximizing entropy is an invariant probabil…

Let $f$ be a $C^r$ diffeomorphism of a closed surface, where $1<r<\infty$, and let $\lambda_{\min}(f)$ denote the minimum expansion rate appearing in the entropy estimates. A measu…