Ergodic Theory Of Expanding Thurston Maps by Zhiqiang LiErgodic Theory Of Expanding Thurston Maps by Zhiqiang Li

Ergodic Theory Of Expanding Thurston Maps

byZhiqiang Li

Hardcover | April 18, 2017

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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 to establish the existence, uniqueness, and various other properties of the equilibrium state for a Holder continuous potential on the sphere equipped with a visual metric. After studying some weak expansion properties of such maps, we obtain certain large deviation principles for iterated preimages and periodic points under an additional assumption on the critical orbits of the maps. This enables us to obtain general equidistribution results for such points with respect to the equilibrium states under the same assumption.
Title:Ergodic Theory Of Expanding Thurston MapsFormat:HardcoverDimensions:182 pagesPublished:April 18, 2017Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9462391734

ISBN - 13:9789462391734

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Table of Contents

1.Introduction.- 2.Thurston maps.- 3.Ergodic theory.- 4.The measure of maximal entropy.- 5.Equilibrium states.- 6.Asymptotic h-Expansiveness.- 7.Large deviation principles.