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200 10$aErgodic theory of expanding Thurston maps$b[electronic resource] /$fby Zhiqiang Li
205   $a1st ed. 2017.
210  1$aParis :$cAtlantis Press :$cImprint: Atlantis Press,$d2017.
215   $a1 online resource (XII, 182 p. 12 illus.)
225 1 $aAtlantis Studies in Dynamical Systems ;$v4
311   $a94-6239-173-4 
320   $aIncludes bibliographical references and index.
327   $a1.Introduction -- 2.Thurston maps -- 3.Ergodic theory -- 4.The measure of maximal entropy -- 5.Equilibrium states -- 6.Asymptotic h-Expansiveness -- 7.Large deviation principles. .
330   $aThurston maps are topological generalizations of postcritically-finite rational maps. This book provides a comprehensive study of ergodic theory of expanding Thurston maps, focusing on the measure of maximal entropy, as well as a more general class of invariant measures, called equilibrium states, and certain weak expansion properties of such maps. In particular, we present equidistribution results for iterated preimages and periodic points with respect to the unique measure of maximal entropy by investigating the number and locations of fixed points. We then use the thermodynamical formalism to establish the existence, uniqueness, and various other properties of the equilibrium state for a Holder continuous potential on the sphere equipped with a visual metric. After studying some weak expansion properties of such maps, we obtain certain large deviation principles for iterated preimages and periodic points under an additional assumption on the critical orbits of the maps. This enables us to obtain general equidistribution results for such points with respect to the equilibrium states under the same assumption.
410  0$aAtlantis Studies in Dynamical Systems ;$v4
606   $aDynamics
606   $aErgodic theory
606   $aFunctions of complex variables
606   $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X
606   $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074
615  0$aDynamics.
615  0$aErgodic theory.
615  0$aFunctions of complex variables.
615 14$aDynamical Systems and Ergodic Theory.
615 24$aFunctions of a Complex Variable.
676   $a515.39
676   $a515.48
700   $aLi$b Zhiqiang$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767421
906   $aBOOK
912   $a9910254279803321
996   $aErgodic Theory of Expanding Thurston Maps$91562347
997   $aUNINA