Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions

DOI10.4171/JST/125zbMath1366.37053arXiv1407.6134MaRDI QIDQ290730

David Borthwick, Tobias Weich

Publication date: 3 June 2016

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.6134

zbMATH Keywords

Selberg zeta functioniterated function scheme

Mathematics Subject Classification ID

Klein surfaces (30F50) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) General geometric structures on low-dimensional manifolds (57M50) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (14)

Resonances for open quantum maps and a fractal uncertainty principle ⋮ Semiclassical formulae for Wigner distributions ⋮ Spectral gaps, additive energy, and a fractal uncertainty principle ⋮ Global normal form and asymptotic spectral gap for open partially expanding maps ⋮ Large degree covers and sharp resonances of hyperbolic surfaces ⋮ Weyl laws for open quantum maps ⋮ Meromorphic continuation of weighted zeta functions on open hyperbolic systems ⋮ Spectral gaps without the pressure condition ⋮ Mathematical study of scattering resonances ⋮ Numerical resonances for Schottky surfaces via Lagrange–Chebyshev approximation ⋮ 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 ⋮ An introduction to fractal uncertainty principle ⋮ Resonance chains and geometric limits on Schottky surfaces

Uses Software

• GAP
• SageMath
• SciPy

Cites Work

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• Sharp geometric upper bounds on resonances for surfaces with hyperbolic ends
• The wave trace for Riemann surfaces
• Resonance chains and geometric limits on Schottky surfaces
• Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum
• Spectral problems in open quantum chaos
• Calculating Hausdorff dimension of Julia sets and Kleinian limit sets
• Spectral theory of infinite-area hyperbolic surfaces

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