<電子ブック>
Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees : Applications to Non-Archimedean Diophantine Approximation / by Anne Broise-Alamichel, Jouni Parkkonen, Frédéric Paulin
(Progress in Mathematics. ISSN:2296505X ; 329)
版 | 1st ed. 2019. |
---|---|
出版者 | (Cham : Springer International Publishing : Imprint: Birkhäuser) |
出版年 | 2019 |
大きさ | VIII, 413 p. 58 illus., 14 illus. in color : online resource |
著者標目 | *Broise-Alamichel, Anne author Parkkonen, Jouni author Paulin, Frédéric author SpringerLink (Online service) |
件 名 | LCSH:Dynamical systems LCSH:Geometry, Differential LCSH:Group theory LCSH:Number theory LCSH:Convex geometry LCSH:Discrete geometry LCSH:Probabilities FREE:Dynamical Systems FREE:Differential Geometry FREE:Group Theory and Generalizations FREE:Number Theory FREE:Convex and Discrete Geometry FREE:Probability Theory |
一般注記 | Introduction -- Negatively curved geometry -- Potentials, critical exponents and Gibbs cocycles -- Patterson-Sullivan and Bowen-Margulis measures with potential on CAT(-1) spaces -- Symbolic dynamics of geodesic flows on trees -- Random walks on weighted graphs of groups -- Skinning measures with potential on CAT(-1) spaces -- Explicit measure computations for simplicial trees and graphs of groups -- Rate of mixing for the geodesic flow -- Equidistribution of equidistant level sets to Gibbs measures -- Equidistribution of common perpendicular arcs -- Equidistribution and counting of common perpendiculars in quotient spaces -- Geometric applications -- Fields with discrete valuations -- Bruhat-Tits trees and modular groups -- Rational point equidistribution and counting in completed function fields -- Equidistribution and counting of quadratic irrational points in non-Archimedean local fields -- Counting and equidistribution of crossratios -- Counting and equidistribution of integral representations by quadratic norm forms -- A - A weak Gibbs measure is the unique equilibrium, by J. Buzzi -- List of Symbols -- Index -- Bibliography 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 quadratic irrationals over function fields in their completions, and asymptotic counting results of the representations by quadratic norm forms. One of the book's main benefits is that the authors provide explicit error terms throughout. Given its scope, it will be of interest to graduate students and researchers in a wide range of fields, for instance ergodic theory, dynamical systems, geometric group theory, discrete subgroups of locally compact groups, and the arithmetic of function fields HTTP:URL=https://doi.org/10.1007/978-3-030-18315-8 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
Springer eBooks | 9783030183158 |
|
電子リソース |
|
EB00196483 |
類似資料
この資料の利用統計
このページへのアクセス回数:1回
※2017年9月4日以降