Ergodic Theory of Expanding Thurston Maps (eBook, PDF)
Zhiqiang Li
eBook, PDF

Ergodic Theory of Expanding Thurston Maps (eBook, PDF)

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Thurston maps are topological generalizations of postcritically-finite rational maps. This book provides a comprehensive study of ergodic theory of expanding Thurston maps, focusing on the measure of maximal entropy, as well as a more general class of invariant measures, called equilibrium states, and certain weak expansion properties of such maps. In particular, we present equidistribution results for iterated preimages and periodic points with respect to the unique measure of maximal entropy by investigating the number and locations of fixed points. We then use the thermodynamical formalism ...

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