03168nam 22005295 450 991025427980332120220404233948.094-6239-174-210.2991/978-94-6239-174-1(CKB)3710000001152102(DE-He213)978-94-6239-174-1(MiAaPQ)EBC4838254(PPN)200510789(EXLCZ)99371000000115210220170406d2017 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierErgodic theory of expanding Thurston maps /by Zhiqiang Li1st ed. 2017.Paris :Atlantis Press :Imprint: Atlantis Press,2017.1 online resource (XII, 182 p. 12 illus.)Atlantis Studies in Dynamical Systems ;494-6239-173-4 Includes bibliographical references and index.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. .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.Atlantis Studies in Dynamical Systems ;4DynamicsErgodic theoryFunctions of complex variablesDynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XFunctions of a Complex Variablehttps://scigraph.springernature.com/ontologies/product-market-codes/M12074Dynamics.Ergodic theory.Functions of complex variables.Dynamical Systems and Ergodic Theory.Functions of a Complex Variable.515.39515.48Li Zhiqiangauthttp://id.loc.gov/vocabulary/relators/aut767421BOOK9910254279803321Ergodic Theory of Expanding Thurston Maps1562347UNINA