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Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees, Anne Broise-Alamichel; Jouni Parkkonen; Fr?d?ric P


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Автор: Anne Broise-Alamichel; Jouni Parkkonen; Fr?d?ric P
Название:  Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees
ISBN: 9783030183141
Издательство: Springer
Классификация:








ISBN-10: 3030183149
Обложка/Формат: Hardcover
Страницы: 413
Вес: 0.80 кг.
Дата издания: 2019
Серия: Progress in Mathematics
Язык: English
Издание: 1st ed. 2019
Иллюстрации: 14 illustrations, color; 44 illustrations, black and white; viii, 413 p. 58 illus., 14 illus. in color.
Размер: 234 x 156 x 24
Читательская аудитория: Professional & vocational
Основная тема: Mathematics
Подзаголовок: Applications to Non-Archimedean Diophantine Approximation
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: 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 books 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.
Дополнительное описание: 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 graph



Equidistribution in Number Theory, An Introduction

Автор: Andrew Granville; Ze?v Rudnick
Название: Equidistribution in Number Theory, An Introduction
ISBN: 1402054033 ISBN-13(EAN): 9781402054037
Издательство: Springer
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Цена: 21661.00 р.
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Описание: Written for graduate students and researchers, this work provides an introduction to the concept of equidistribution in number theory, which is of importance in many areas, including cryptography, zeros of L-functions, Heegner points, prime number theory, the theory of quadratic forms, and the arithmetic aspects of quantum chaos.

Analytic and Probabilistic Approaches to Dynamics in Negative Curvature

Автор: Fran?oise Dal`Bo; Marc Peign?; Andrea Sambusetti
Название: Analytic and Probabilistic Approaches to Dynamics in Negative Curvature
ISBN: 3319381172 ISBN-13(EAN): 9783319381176
Издательство: Springer
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Цена: 11878.00 р.
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Описание: The work consists of two introductory courses, developing different points of view on the study of the asymptotic behaviour of the geodesic flow, namely: the probabilistic approach via martingales and mixing (by Stephane Le Borgne);

Mean Curvature Flow: Proceedings of the John H. Barrett Memorial Lectures held at the University of Tennessee, Knoxville, May 29 - June 1, 2018

Автор: Theodora Bourni, Mat Langford
Название: Mean Curvature Flow: Proceedings of the John H. Barrett Memorial Lectures held at the University of Tennessee, Knoxville, May 29 - June 1, 2018
ISBN: 3110618184 ISBN-13(EAN): 9783110618181
Издательство: Walter de Gruyter
Цена: 19330.00 р.
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Описание:

With contributions by leading experts in geometric analysis, this volume is documenting the material presented in the John H. Barrett Memorial Lectures held at the University of Tennessee, Knoxville, on May 29 - June 1, 2018. The central topic of the 2018 lectures was mean curvature flow, and the material in this volume covers all recent developments in this vibrant area that combines partial differential equations with differential geometry.

Geometry of Manifolds with Non-negative Sectional Curvature

Автор: Owen Dearricott; Fernando Galaz-Garc?a; Lee Kennar
Название: Geometry of Manifolds with Non-negative Sectional Curvature
ISBN: 3319063723 ISBN-13(EAN): 9783319063720
Издательство: Springer
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Цена: 4890.00 р.
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Описание:

Riemannian manifolds with positive sectional curvature.- An introduction to isometric group actions.- A note on maximal symmetry rank, quasipositive curvature and low dimensional manifolds.- Lectures on n-Sasakian manifolds.- On the Hopf conjecture with symmetry.- An Introduction to Exterior Differential Systems.

Geometry, Topology, and Dynamics in Negative Curvature

Автор: Aravinda
Название: Geometry, Topology, and Dynamics in Negative Curvature
ISBN: 110752900X ISBN-13(EAN): 9781107529007
Издательство: Cambridge Academ
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Цена: 11405.00 р.
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Описание: Negative curvature arises in several mathematical areas, including geometry, topology, dynamics, and number theory. This volume contains survey articles around this common theme, which should help mathematicians interested in transitioning between these areas, as well as graduate students entering this interdisciplinary subject.

Brakke`s Mean Curvature Flow

Автор: Yoshihiro Tonegawa
Название: Brakke`s Mean Curvature Flow
ISBN: 9811370745 ISBN-13(EAN): 9789811370748
Издательство: Springer
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Цена: 6986.00 р.
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Описание: This book explains the notion of Brakke`s mean curvature flow and its existence and regularity theories without assuming familiarity with geometric measure theory.

Complete Minimal Surfaces of Finite Total Curvature

Автор: Kichoon Yang
Название: Complete Minimal Surfaces of Finite Total Curvature
ISBN: 0792330129 ISBN-13(EAN): 9780792330127
Издательство: Springer
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Цена: 10760.00 р.
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Описание: Based on the idea that the study of complete minimal surfaces in R3 of finite total curvature amounts to the study of linear series on algebraic curves, this book offers an account of the Puncture Number Problem, which seeks to determine the possible underlying conformal structures for immersed complete minimal surfaces of finite total curvature.

Metric Spaces of Non-Positive Curvature

Автор: Martin R. Bridson; Andr? H?fliger
Название: Metric Spaces of Non-Positive Curvature
ISBN: 3642083994 ISBN-13(EAN): 9783642083990
Издательство: Springer
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Цена: 16769.00 р.
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Описание: The purpose of this book is to describe the global properties of complete simply- connected spaces that are non-positively curved in the sense of A. D. Alexandrov and to examine the structure of groups that act properly on such spaces by isometries. Thus the central objects of study are metric spaces in which every pair of points can be joined by an arc isometric to a compact interval of the real line and in which every triangle satisfies the CAT(O) inequality. This inequality encapsulates the concept of non-positive curvature in Riemannian geometry and allows one to reflect the same concept faithfully in a much wider setting - that of geodesic metric spaces. Because the CAT(O) condition captures the essence of non-positive curvature so well, spaces that satisfy this condition display many of the elegant features inherent in the geometry of non-positively curved manifolds. There is therefore a great deal to be said about the global structure of CAT(O) spaces, and also about the structure of groups that act on them by isometries - such is the theme of this book. 1 The origins of our study lie in the fundamental work of A. D. Alexandrov .

Total Mean Curvature and Submanifolds of Finite Type: 2nd Edition

Автор: Chen Bang-Yen
Название: Total Mean Curvature and Submanifolds of Finite Type: 2nd Edition
ISBN: 9814616699 ISBN-13(EAN): 9789814616690
Издательство: World Scientific Publishing
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Цена: 7128.00 р.
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Описание: During the last four decades, there were numerous important developments on total mean curvature and the theory of finite type submanifolds.


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