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- W4300142834 abstract "Let $f:Xto X$ be a continuous map on a compact metric space with finite topological entropy. Further, we assume that the entropy map $mumapsto h_mu(f)$ is upper semi-continuous. It is well-known that this implies the continuity of the localized entropy function of a given continuous potential $phi:Xto R$. In this note we show that this result does not carry over to the case of higher-dimensional potentials $Phi:Xto R^m$. Namely, we construct for a shift map $f$ a $2$-dimensional Lipschitz continuous potential $Phi$ with a discontinuous localized entropy function." @default.
- W4300142834 created "2022-10-03" @default.
- W4300142834 creator A5015837326 @default.
- W4300142834 date "2018-03-06" @default.
- W4300142834 modified "2023-09-28" @default.
- W4300142834 title "A shift map with a discontinuous entropy function" @default.
- W4300142834 doi "https://doi.org/10.48550/arxiv.1803.02440" @default.
- W4300142834 hasPublicationYear "2018" @default.
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