Ergodic theory of expanding Thurston maps / Zhiqiang Li.
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, a...
Saved in:
| Main Author: | |
|---|---|
| Format: | Ebook |
| Language: | English |
| Published: |
[Paris] :
Atlantis Press,
2017.
|
| Series: | Atlantis series in dynamical systems ;
v. 4. |
| Subjects: | |
| Online Access: | Springer eBooks |
MARC
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| 100 | 1 | |a Li, Zhiqiang, |e author. |9 884551 | |
| 245 | 1 | 0 | |a Ergodic theory of expanding Thurston maps / |c Zhiqiang Li. |
| 264 | 1 | |a [Paris] : |b Atlantis Press, |c 2017. | |
| 300 | |a 1 online resource (xii, 182 pages) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Atlantis studies in dynamical systems ; |v volume 4 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Preface; Contents; Notation; 1 Introduction; 2 Thurston Maps; 2.1 Historical Background; 2.2 Definition for Thurston Maps; 2.3 Cell Decompositions; 2.4 Notions of Expansion for Thurston Maps; 2.5 Visual Metric; 2.6 Invariant Curves; 3 Ergodic Theory; 3.1 Covers and Partitions; 3.2 Entropy and Pressure; 3.3 The Ruelle Operator for Expanding Thurston Maps; 3.4 Weak Expansion Properties; 4 The Measure of Maximal Entropy; 4.1 Number and Locations of Fixed Points; 4.2 Equidistribution; 4.3 Expanding Thurston Maps as Factors of the Left-Shift; 5 Equilibrium States; 5.1 The Assumptions. | |
| 520 | |a 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. | ||
| 538 | |a Mode of access: World Wide Web. | ||
| 588 | 0 | |a Online resource; title from PDF title page (EBSCO, viewed April 13, 2017). | |
| 650 | 0 | |a Ergodic theory. |9 330420 | |
| 776 | 0 | 8 | |i Print version: |a Li, Zhiqiang. |t Ergodic theory of expanding Thurston maps. |d [Paris] : Atlantis Press, 2017 |z 9789462391734 |z 9462391734 |w (OCoLC)930257963 |
| 776 | 1 | 8 | |w (OCoLC)982143984 |w (OCoLC)982225567 |w (OCoLC)982338873 |w (OCoLC)982408078 |w (OCoLC)982613869 |w (OCoLC)988379128 |
| 830 | 0 | |a Atlantis series in dynamical systems ; |v v. 4. |9 861027 | |
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