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- W2972936324 abstract "Given a closed, oriented, compact surface $S$ of constant negative curvature and genus $g ge 2$, we study the measure-theoretic entropy of the Bowen-Series boundary map with respect to its smooth invariant measure. We obtain an explicit formula for the entropy that only depends on the perimeter of the $(8g-4)$-sided fundamental polygon of the surface $S$ and its genus. Using this, we analyze how the entropy changes in the Teichmuller space of $S$ and prove the following flexibility result: the measure-theoretic entropy takes all values between $0$ and a maximum that is achieved on the surface that admits a regular $(8g-4)$-sided fundamental polygon. We also compare the measure-theoretic entropy to the topological entropy of these maps and show that the smooth invariant measure is not the measure of maximal entropy." @default.
- W2972936324 created "2019-09-19" @default.
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- W2972936324 date "2019-09-16" @default.
- W2972936324 modified "2023-09-27" @default.
- W2972936324 title "Flexibility of entropy of boundary maps for surfaces of constant negative curvatures" @default.
- W2972936324 hasPublicationYear "2019" @default.
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