| 書目名稱 | Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees | | 副標(biāo)題 | Applications to Non- | | 編輯 | Anne Broise-Alamichel,Jouni Parkkonen,Frédéric Pau | | 視頻video | http://file.papertrans.cn/314/313467/313467.mp4 | | 概述 | Introduces innovative ergodic techniques to Diophantine approximation in non-Archimedean local fields.Gives numerous first published error terms in geometric counting and equidistribution problems.Bri | | 叢書名稱 | Progress in Mathematics | | 圖書封面 |  | | 描述 | .This book provides a complete exposition of equidistribution and counting problems weighted by a potential function of common perpendicular geodesics in negatively curved manifolds and simplicial trees. Avoiding any compactness assumptions, the authors extend the theory of Patterson-Sullivan, Bowen-Margulis and Oh-Shah (skinning) measures to CAT(-1) spaces with potentials. The work presents a proof for the equidistribution of equidistant hypersurfaces to Gibbs measures, and the equidistribution of common perpendicular arcs between, for instance, closed geodesics. Using tools from ergodic theory (including coding by topological Markov shifts, and an appendix by Buzzi that relates weak Gibbs measures and equilibrium states for them), the authors further prove the variational principle and rate of mixing for the geodesic flow on metric and simplicial trees—again without the need for any compactness or torsionfree assumptions..In a series of applications, using the Bruhat-Tits trees over non-Archimedean local fields, the authors subsequently prove further important results: the Mertens formula and the equidistribution of Farey fractions in function fields, the equidistribution of quad | | 出版日期 | Book 2019 | | 關(guān)鍵詞 | equidistribution; orbit counting; geodesic flow; negative curvature; common perpendicular; ortholength sp | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-18315-8 | | isbn_softcover | 978-3-030-18317-2 | | isbn_ebook | 978-3-030-18315-8Series ISSN 0743-1643 Series E-ISSN 2296-505X | | issn_series | 0743-1643 | | copyright | Springer Nature Switzerland AG 2019 |
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