Ergodic Theory of Expanding Thurston Maps (Hardcover, 1st ed. 2017)

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.

General

Imprint:	Atlantis Press (Zeger Karssen)
Country of origin:	Netherlands
Series:	Atlantis Studies in Dynamical Systems, 4
Release date:	April 2017
First published:	2017
Authors:	Zhiqiang Li
Dimensions:	235 x 155 x 13mm (L x W x T)
Format:	Hardcover
Pages:	182
Edition:	1st ed. 2017
ISBN-13:	978-9462391734
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations Books > Science & Mathematics > Mathematics > Applied mathematics > Non-linear science
LSN:	9462391734
Barcode:	9789462391734

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