Some applications of thermodynamic formalism to manifolds with constant negative curvature

DOI10.1016/0001-8708(91)90054-BzbMath0726.58047OpenAlexW2021890214MaRDI QIDQ804052

Mark Pollicott

Publication date: 1991

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(91)90054-b

zbMATH Keywords

spectrumSelberg trace formulalimit setsKleinian groupsGibbs statescompact surface of constant negative curvatureMarkov covers

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40)

Related Items (25)

Invariant relations for the Bowen-Series transform ⋮ Hecke triangle groups, transfer operators and Hausdorff dimension ⋮ Zeta functions and periodic orbit theory: A review ⋮ Towards a semiclassical theory of the quantum Baker's map ⋮ Hyperbolic systems, zeta functions and other friends ⋮ Symbolic dynamics for the geodesic flow on two-dimensional hyperbolic good orbifolds ⋮ Ergodic transport theory and piecewise analytic subactions for analytic dynamics ⋮ Large degree covers and sharp resonances of hyperbolic surfaces ⋮ Intertwining the geodesic flow and the Schrödinger group on hyperbolic surfaces ⋮ Meromorphic extension of the Selberg zeta function for Kleinian groups via thermodynamic formalism ⋮ The Selberg zeta function for convex co-compact Schottky groups ⋮ Density and location of resonances for convex co-compact hyperbolic surfaces ⋮ On the Ruelle eigenvalue sequence ⋮ Period functions for Hecke triangle groups, and the Selberg zeta function as a Fredholm determinant ⋮ Expanding maps on Cantor sets and analytic continuation of zeta functions ⋮ Distribution of Resonances for Hyperbolic Surfaces ⋮ A thermodynamic formalism approach to the Selberg zeta function for Hecke triangle surfaces of infinite area ⋮ The thermodynamic formalism approach to Selberg’s zeta function for 𝑃𝑆𝐿(2,𝐙) ⋮ Odd and even Maass cusp forms for Hecke triangle groups, and the billiard flow ⋮ Meromorphic continuation of Selberg zeta functions with twists having non-expanding cusp monodromy ⋮ Kleinian Groups, Laplacian on Forms and Currents at Infinity ⋮ A transfer-operator-based relation between Laplace eigenfunctions and zeros of Selberg zeta functions ⋮ Zeros of the Selberg zeta function for symmetric infinite area hyperbolic surfaces ⋮ Quantum maps from transfer operators ⋮ Dynamics of the continued fraction map and the spectral theory of \(\text{SL}(2,\mathbb{Z})\)

Cites Work

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