| 书目名称 | Ergodic Theory of Expanding Thurston Maps |
| 编辑 | Zhiqiang Li |
| 视频video | |
| 概述 | 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.Includes supp |
| 丛书名称 | Atlantis Studies in Dynamical Systems |
| 图书封面 |  |
| 描述 | 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. |
| 出版日期 | Book 2017 |
| 关键词 | Thurston Map; Postcritically-finite Map; Nonuniformly Expanding Map; Thermodynamical Formalism; Equilibr |
| 版次 | 1 |
| doi | https://doi.org/10.2991/978-94-6239-174-1 |
| isbn_ebook | 978-94-6239-174-1Series ISSN 2213-3526 Series E-ISSN 2213-3534 |
| issn_series | 2213-3526 |
| copyright | Atlantis Press and the author(s) 2017 |
发表于 2025-3-21 17:18:04
