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Atlantis Studies in Dynamical Systems

Ergodic Theory of Expanding Thurston Maps

Authors: Li, Zhiqiang

  • A comprehensive study of ergodic theory of expanding Thurston maps
    The proofs are written with a non-specialist audience in mind
    Develop thermodynamical formalism for a new class of maps

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eBook $69.99
price for USA (gross)
  • ISBN 978-94-6239-174-1
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  • Immediate eBook download after purchase
Hardcover $89.99
price for USA
  • ISBN 978-94-6239-173-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Table of contents (7 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-94-6239-174-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA
  • ISBN 978-94-6239-173-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Ergodic Theory of Expanding Thurston Maps
Authors
Series Title
Atlantis Studies in Dynamical Systems
Series Volume
4
Copyright
2017
Publisher
Atlantis Press
Copyright Holder
Atlantis Press and the author(s)
eBook ISBN
978-94-6239-174-1
DOI
10.2991/978-94-6239-174-1
Hardcover ISBN
978-94-6239-173-4
Edition Number
1
Number of Pages
XII, 182
Number of Illustrations and Tables
12 b/w illustrations
Topics