Upper bound on the density of Ruelle resonances for Anosov flows

Abstract

Using a semiclassical approach we show that the spectrum of a smooth Anosov vector field V on a compact manifold is discrete (in suitable anisotropic Sobolev spaces) and then we provide an upper bound for the density of eigenvalues of the operator (-i)V, called Ruelle resonances, close to the real axis and for large real parts.

57 pages

References in corpus (5)

• The Selberg zeta function for convex co-compact Schottky groups
• Ruelle-Pollicott resonances for real analytic hyperbolic map
• Distribution of resonances for open quantum maps
• Periodic orbit spectrum in terms of Ruelle--Pollicott resonances
• Some open questions in "wave chaos"

Cited by in corpus (32)

• Pollicott-Ruelle resonances for open systems
• Ruelle zeta function at zero for surfaces
• Resonance projectors and asymptotics for r-normally hyperbolic trapped sets
• Power spectrum of the geodesic flow on hyperbolic manifolds
• Stochastic stability of Pollicott-Ruelle resonances
• Fried conjecture in small dimensions
• Sharp polynomial bounds on the number of Pollicott-Ruelle resonances
• The Feynman propagator on perturbations of Minkowski space
• Pollicott-Ruelle resonant states and Betti numbers
• Dynamical zeta functions for Axiom A flows
• Geodesic stretch, pressure metric and marked length spectrum rigidity
• Horocycle averages on closed manifolds and transfer operators
• The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds
• On the spectra of quenched random perturbations of partially expanding maps on the torus
• Semiclassical Formulae For Wigner Distributions
• Higher rank quantum-classical correspondence
• Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps
• Isometric extensions of Anosov flows via microlocal analysis
• A paradifferential approach for hyperbolic dynamical systems and applications
• Dynamical torsion for contact Anosov flows
• Flat trace statistics of the transfer operator of a random partially expanding map
• On the s-injectivity of the X-ray transform on manifolds with hyperbolic trapped set
• On the support of Pollicott-Ruelle resonant states for Anosov flows
• Global trace formula for ultra-differentiable Anosov flows
• Scattering theory for repulsive Schrödinger operators and applications to limit circle problem
• Fractal Weyl laws and wave decay for general trapping
• Resonant forms at zero for dissipative Anosov flows
• Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature
• Anosov vector fields and Fried sections
• Kolmogorov Modes and Linear Response of Jump-Diffusion Models
• Resolvent of vector fields and Lefschetz numbers
• Perturbative BF theory in axial, Anosov, gauge