Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees Applications to Non-Archimedean Diophantine Approximation /

• Main Authors: Broise-Alamichel, Anne (Author, http://id.loc.gov/vocabulary/relators/aut), Parkkonen, Jouni (http://id.loc.gov/vocabulary/relators/aut), Paulin, Frédéric (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2019.
• Edition: 1st ed. 2019.
• Series: Progress in Mathematics, 329
• Subjects: Dynamics.; Ergodic theory.; Differential geometry.; Group theory.; Number theory.; Convex geometry .; Discrete geometry.; Probabilities.; Dynamical Systems and Ergodic Theory.; Differential Geometry.; Group Theory and Generalizations.; Number Theory.; Convex and Discrete Geometry.; Probability Theory and Stochastic Processes.

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-...

Table of Contents:

• 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.