Ergodic Theory of Expanding Thurston Maps

Zhiqiang Li (Autor)

Buch | Hardcover

182 Seiten

2017 | 2017 ed.
Atlantis Press (Zeger Karssen) (Verlag)
978-94-6239-173-4 (ISBN)

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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 enablesus to obtain general equidistribution results for such points with respect to the equilibrium states under the same assumption.

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.

Erscheinungsdatum	29.04.2017
Reihe/Serie	Atlantis Studies in Dynamical Systems ; 4
Zusatzinfo	12 Illustrations, black and white; XII, 182 p. 12 illus.
Verlagsort	Paris
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Equilibrium State • Nonuniformly Expanding Map • Postcritically-finite Map • thermodynamical formalism • Thurston Map
ISBN-10	94-6239-173-4 / 9462391734
ISBN-13	978-94-6239-173-4 / 9789462391734
Zustand	Neuware