Nonlinearity, ISSN 0951-7715, 09/2018, Volume 31, Issue 10, pp. 4667 - 4691

We investigate the dynamics close to a homogeneous stationary state of the Vlasov equation in one dimension, in presence of a small dissipation modeled by a...

stochastic stability | bifurcation | Landau damping | Bargmann representation | Mellin transform | Vlasov-Fokker-Planck equation | MATHEMATICS, APPLIED | INSTABILITY | BEHAVIOR | FREE SHEAR-LAYER | KURAMOTO MODEL | PHYSICS, MATHEMATICAL | SPACE | WAVES | PLASMA-OSCILLATIONS | NONLINEAR STABILITY | GLOBALLY-COUPLED OSCILLATORS | POLLICOTT-RUELLE RESONANCES

stochastic stability | bifurcation | Landau damping | Bargmann representation | Mellin transform | Vlasov-Fokker-Planck equation | MATHEMATICS, APPLIED | INSTABILITY | BEHAVIOR | FREE SHEAR-LAYER | KURAMOTO MODEL | PHYSICS, MATHEMATICAL | SPACE | WAVES | PLASMA-OSCILLATIONS | NONLINEAR STABILITY | GLOBALLY-COUPLED OSCILLATORS | POLLICOTT-RUELLE RESONANCES

Journal Article

Analysis and PDE, ISSN 2157-5045, 2015, Volume 8, Issue 4, pp. 923 - 1000

.... These poles are a special case of Pollicott-Ruelle resonances, which can be defined for general Anosov flows...

Hyperbolic manifolds | Pollicott-Ruelle resonances | MATHEMATICS, APPLIED | SELBERG ZETA-FUNCTION | DECAY | SPACES | INVARIANT | EIGENFUNCTIONS | hyperbolic manifolds | ANOSOV-FLOWS | DISTRIBUTIONS | LAPLACIAN | MATHEMATICS | OPERATORS

Hyperbolic manifolds | Pollicott-Ruelle resonances | MATHEMATICS, APPLIED | SELBERG ZETA-FUNCTION | DECAY | SPACES | INVARIANT | EIGENFUNCTIONS | hyperbolic manifolds | ANOSOV-FLOWS | DISTRIBUTIONS | LAPLACIAN | MATHEMATICS | OPERATORS

Journal Article

Nonlinearity, ISSN 0951-7715, 11/2017, Volume 30, Issue 12, pp. 4301 - 4343

We prove a Weyl upper bound on the number of scattering resonances in strips for manifolds with Euclidean infinite ends...

wave decay | resonances | Weyl law | MATHEMATICS, APPLIED | NUMBER | PHYSICS, MATHEMATICAL | DENSITY | MICROLOCAL ANALYSIS | UPPER-BOUNDS | MAPS | POLLICOTT-RUELLE RESONANCES | FLOWS | OPEN SYSTEMS

wave decay | resonances | Weyl law | MATHEMATICS, APPLIED | NUMBER | PHYSICS, MATHEMATICAL | DENSITY | MICROLOCAL ANALYSIS | UPPER-BOUNDS | MAPS | POLLICOTT-RUELLE RESONANCES | FLOWS | OPEN SYSTEMS

Journal Article

Annales Scientifiques de l'Ecole Normale Superieure, ISSN 0012-9593, 2016, Volume 49, Issue 3, pp. 543 - 577

The purpose of this paper is to give a short microlocal proof of the meromorphic continuation of the Ruelle zeta function for C-infinity Anosov flows. More...

DIFFEOMORPHISMS | MATHEMATICS | SOBOLEV SPACES | NUMBER | POLLICOTT-RUELLE RESONANCES | RIEMANN SURFACES | SYSTEMS | HYPERBOLIC MANIFOLDS | SPECTRUM | OPERATORS | FREDHOLM DETERMINANTS

DIFFEOMORPHISMS | MATHEMATICS | SOBOLEV SPACES | NUMBER | POLLICOTT-RUELLE RESONANCES | RIEMANN SURFACES | SYSTEMS | HYPERBOLIC MANIFOLDS | SPECTRUM | OPERATORS | FREDHOLM DETERMINANTS

Journal Article

Nonlinearity, ISSN 0951-7715, 09/2015, Volume 28, Issue 10, pp. 3511 - 3533

Pollicott-Ruelle resonances for chaotic flows are the characteristic frequencies of correlations...

Anosov flow | decay of correlations | Pollicott-Ruelle resonances | MATHEMATICS, APPLIED | ANOSOV | MAPS | SPACES | SETS | SPECTRUM | PHYSICS, MATHEMATICAL | Viscosity | Operators | Correlation | Stability | Probability theory | Eigenvalues | Nonlinearity | Stochasticity

Anosov flow | decay of correlations | Pollicott-Ruelle resonances | MATHEMATICS, APPLIED | ANOSOV | MAPS | SPACES | SETS | SPECTRUM | PHYSICS, MATHEMATICAL | Viscosity | Operators | Correlation | Stability | Probability theory | Eigenvalues | Nonlinearity | Stochasticity

Journal Article

Annales Henri Poincaré, ISSN 1424-0637, 1/2017, Volume 18, Issue 1, pp. 1 - 35

We prove a local trace formula for Anosov flows. It relates Pollicott–Ruelle resonances to the periods of closed orbits...

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | DIFFEOMORPHISMS | NUMBER | ZETA-FUNCTIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | AXIOM | DYNAMICAL-SYSTEMS | BOUNDS | POLLICOTT-RUELLE RESONANCES | POLES | SPECTRUM | OPERATORS | PHYSICS, PARTICLES & FIELDS

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | DIFFEOMORPHISMS | NUMBER | ZETA-FUNCTIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | AXIOM | DYNAMICAL-SYSTEMS | BOUNDS | POLLICOTT-RUELLE RESONANCES | POLES | SPECTRUM | OPERATORS | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 11/2002, Volume 109, Issue 3, pp. 777 - 801

.... The scattering resonances of the corresponding hierarchical quantum graphs are also studied. The width distribution shows the scaling behavior P(Γ)∼1/Γ.

Physical Chemistry | Mathematical and Computational Physics | Pollicott–Ruelle resonances | Quantum Physics | Survival probability | quantum scattering resonances | algebraic decay | Physics | Statistical Physics | Pollicott-Ruelle resonances | Quantum scattering resonances | Algebraic decay | DYNAMICAL CHAOS | PHYSICS, MATHEMATICAL | TRANSPORT | CHAOTIC SCATTERING-THEORY | MARKOV-TREE MODEL | MAPS | CONDUCTANCE FLUCTUATIONS | survival probability | Pollicott- Ruelle resonances | QUANTIZATION | RESONANCES | Physics - Chaotic Dynamics

Physical Chemistry | Mathematical and Computational Physics | Pollicott–Ruelle resonances | Quantum Physics | Survival probability | quantum scattering resonances | algebraic decay | Physics | Statistical Physics | Pollicott-Ruelle resonances | Quantum scattering resonances | Algebraic decay | DYNAMICAL CHAOS | PHYSICS, MATHEMATICAL | TRANSPORT | CHAOTIC SCATTERING-THEORY | MARKOV-TREE MODEL | MAPS | CONDUCTANCE FLUCTUATIONS | survival probability | Pollicott- Ruelle resonances | QUANTIZATION | RESONANCES | Physics - Chaotic Dynamics

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 10/2000, Volume 101, Issue 1, pp. 161 - 186

We apply the hypothesis of microscopic chaos to diffusion-controlled reaction which we study in a reactive periodic Lorentz gas. The relaxation rate of the...

diffusion-controlled reaction | Frobenius–Perron operator | dynamical chaos | isomerization | Mathematical and Computational Physics | Quantum Physics | reaction rate | Physics | Poincaré–Birkhoff map | Physical Chemistry | Pollicott–Ruelle resonances | Lebesgue singular function | random-walk | Statistical Physics | reactive Lorentz gas | cross-diffusion | Cross-diffusion | Reactive Lorentz gas | Random-walk | Diffusion-controlled reaction | Frobenius-Perron operator | Isomerization | Dynamical chaos | Poincaré-Birkhoff map | Reaction rate | Pollicott Ruelle resonances | Poincare-Birkhoff map | Pollicott-Ruelle resonances | SCATTERING-THEORY | PHYSICS, MATHEMATICAL | DETERMINISTIC DIFFUSION | TRANSPORT | COEFFICIENTS

diffusion-controlled reaction | Frobenius–Perron operator | dynamical chaos | isomerization | Mathematical and Computational Physics | Quantum Physics | reaction rate | Physics | Poincaré–Birkhoff map | Physical Chemistry | Pollicott–Ruelle resonances | Lebesgue singular function | random-walk | Statistical Physics | reactive Lorentz gas | cross-diffusion | Cross-diffusion | Reactive Lorentz gas | Random-walk | Diffusion-controlled reaction | Frobenius-Perron operator | Isomerization | Dynamical chaos | Poincaré-Birkhoff map | Reaction rate | Pollicott Ruelle resonances | Poincare-Birkhoff map | Pollicott-Ruelle resonances | SCATTERING-THEORY | PHYSICS, MATHEMATICAL | DETERMINISTIC DIFFUSION | TRANSPORT | COEFFICIENTS

Journal Article

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