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- W2198855982 abstract "In this paper, we prove that an expanding Thurston map $fcolon S^2 rightarrow S^2$ is asymptotically $h$-expansive if and only if it has no periodic critical points, and that no expanding Thurston map is $h$-expansive. As a consequence, for each expanding Thurston map without periodic critical points and each real-valued continuous potential on $S^2$, there exists at least one equilibrium state. For such maps, we also establish large deviation principles for iterated preimages and periodic points. It follows that iterated preimages and periodic points are equidistributed with respect to the unique equilibrium state for an expanding Thurston map without periodic critical points and a potential that is Holder continuous with respect to a visual metric on $S^2$." @default.
- W2198855982 created "2016-06-24" @default.
- W2198855982 creator A5074461919 @default.
- W2198855982 date "2015-01-31" @default.
- W2198855982 modified "2023-09-24" @default.
- W2198855982 title "Weak expansion properties and large deviation principles for expanding Thurston maps" @default.
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- W2198855982 doi "https://doi.org/10.48550/arxiv.1502.00153" @default.
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