Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees
portes grátis
Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees
Applications to Non-Archimedean Diophantine Approximation
Parkkonen, Jouni; Broise-Alamichel, Anne; Paulin, Frederic
Springer Nature Switzerland AG
01/2020
413
Dura
Inglês
9783030183141
15 a 20 dias
799
Descrição não disponível.
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.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
equidistribution;orbit counting;geodesic flow;negative curvature;common perpendicular;ortholength spectrum;equilibrium state;Gibbs measure;skinning measure
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.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
