Sharp polynomial bounds on the number of Pollicott–Ruelle resonances

DOI10.1017/etds.2013.3zbMath1332.37006arXiv1208.4330OpenAlexW2154719177MaRDI QIDQ2925261

Semyon Dyatlov, Maciej Zworski, Kiril Datchev

Publication date: 21 October 2014

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.4330

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (13)

Pollicott-Ruelle resonances for open systems ⋮ Band structure of the Ruelle spectrum of contact Anosov flows ⋮ Geodesic flows on negatively curved manifolds and the semi-classical zeta function ⋮ Stochastic stability of Pollicott-Ruelle resonances ⋮ Fractal Weyl law for the Ruelle spectrum of Anosov flows ⋮ Higher rank quantum-classical correspondence ⋮ Fractal Weyl laws and wave decay for general trapping ⋮ A local trace formula for Anosov flows ⋮ High frequency limits for invariant Ruelle densities ⋮ Resonance projectors and asymptotics for 𝑟-normally hyperbolic trapped sets ⋮ Decay of correlations for normally hyperbolic trapping ⋮ Spectral Properties of Ruelle Transfer Operators for Regular Gibbs Measures and Decay of Correlations for Contact Anosov Flows ⋮ The semiclassical zeta function for geodesic flows on negatively curved manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Upper bound on the density of Ruelle resonances for Anosov flows
• Fractal upper bounds on the density of semiclassical resonances
• Geometric bounds on the density of resonances for semiclassical problems
• Sharp polynomial bounds on the number of scattering poles
• On the wave equation on a compact Riemannian manifold without conjugate points
• Sharp bounds on the number of scattering poles in even-dimensional spaces
• On contact Anosov flows
• Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms
• Smooth Anosov flows: Correlation spectra and stability
• Fredholm determinants, Anosov maps and Ruelle resonances
• Quasi-compactness of transfer operators for contact Anosov flows
• Espaces fonctionnels associés au calcul de Weyl-Hörmander
• Ruelle Perron Frobenius spectrum for Anosov maps

This page was built for publication: Sharp polynomial bounds on the number of Pollicott–Ruelle resonances