Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees

Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees

Applications to Non-Archimedean Diophantine Approximation

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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 theor...