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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees: Applications to Non-Archimedean Diophantine Approximation

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

Broise-Alamichel, Anne
Parkkonen, Jouni
Paulin, Frédéric

Hardcover

Series: Progress in Mathematics, Book 329

AlgebraGeneral MathematicsGeometry

ISBN10: 3030183149
ISBN13: 9783030183141
Publisher: Birkhauser
Published: Jan 2 2020
Pages: 413
Weight: 1.69
Height: 0.94 Width: 6.14 Depth: 9.21
Language: English

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.

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