Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees Applications to Non-Archimedean Diophantine Approximation /
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-...
Κύριοι συγγραφείς: | , , |
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Συγγραφή απο Οργανισμό/Αρχή: | |
Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
Γλώσσα: | English |
Έκδοση: |
Cham :
Springer International Publishing : Imprint: Birkhäuser,
2019.
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Έκδοση: | 1st ed. 2019. |
Σειρά: | Progress in Mathematics,
329 |
Θέματα: | |
Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- 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.