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Titlebook: Ergodic Theory of Expanding Thurston Maps; Zhiqiang Li Book 2017 Atlantis Press and the author(s) 2017 Thurston Map.Postcritically-finite

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發(fā)表于 2025-3-21 17:18:04 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Ergodic Theory of Expanding Thurston Maps
編輯Zhiqiang Li
視頻videohttp://file.papertrans.cn/315/314497/314497.mp4
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
叢書名稱Atlantis Studies in Dynamical Systems
圖書封面Titlebook: Ergodic Theory of Expanding Thurston Maps;  Zhiqiang Li Book 2017 Atlantis Press and the author(s) 2017 Thurston Map.Postcritically-finite
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
關(guān)鍵詞Thurston Map; Postcritically-finite Map; Nonuniformly Expanding Map; Thermodynamical Formalism; Equilibr
版次1
doihttps://doi.org/10.2991/978-94-6239-174-1
isbn_ebook978-94-6239-174-1Series ISSN 2213-3526 Series E-ISSN 2213-3534
issn_series 2213-3526
copyrightAtlantis Press and the author(s) 2017
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沙發(fā)
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Louise Roberts,Daniel R. HowardThis Chapter is devoted to the investigation of the weak expansion properties of expanding Thurston maps and the proof of Theorem?. that asserts that an expanding Thurston map is asymptotically .-expansive if and only if . has no periodic critical points, and moreover, it is never .-expansive.
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發(fā)表于 2025-3-22 12:09:23 | 只看該作者
Asymptotic ,-Expansiveness,This Chapter is devoted to the investigation of the weak expansion properties of expanding Thurston maps and the proof of Theorem?. that asserts that an expanding Thurston map is asymptotically .-expansive if and only if . has no periodic critical points, and moreover, it is never .-expansive.
6#
發(fā)表于 2025-3-22 14:34:48 | 只看該作者
https://doi.org/10.1007/978-981-10-9029-5r naturally in mathematics and play important roles in the investigation of the corresponding areas of research. One particularly abundant source of self-similar fractals is the study of holomorphic dynamics, where they arise as Julia sets of rational functions and limit sets of Kleinian groups.
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發(fā)表于 2025-3-22 18:33:22 | 只看該作者
8#
發(fā)表于 2025-3-23 00:32:20 | 只看該作者
Zhiqiang LiA 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
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發(fā)表于 2025-3-23 04:39:33 | 只看該作者
10#
發(fā)表于 2025-3-23 06:14:57 | 只看該作者
https://doi.org/10.1007/978-981-10-9029-5r naturally in mathematics and play important roles in the investigation of the corresponding areas of research. One particularly abundant source of self-similar fractals is the study of holomorphic dynamics, where they arise as Julia sets of rational functions and limit sets of Kleinian groups.
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