12/2015

We give a new fractal Weyl upper bound for resonances of convex co-compact hyperbolic manifolds in terms of the dimension $n$ of the manifold and the dimension...

Journal Article

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, ISSN 1435-9855, 2019, Volume 21, Issue 6, pp. 1595 - 1639

We give a new fractal Weyl upper bound for resonances of convex co-compact hyperbolic manifolds in terms of the dimension n of the manifold and the dimension...

MATHEMATICS | MATHEMATICS, APPLIED | fractal Weyl law | MAPS | Resonances | hyperbolic quotients

MATHEMATICS | MATHEMATICS, APPLIED | fractal Weyl law | MAPS | Resonances | hyperbolic quotients

Journal Article

Journal of mathematical physics, ISSN 1089-7658, 2019, Volume 60, Issue 8, p. 081505

Fractal uncertainty principle states that no function can be localized in both position and frequency near a fractal set. This article provides a review of...

SPECTRAL GAPS | LAPLACIAN | ANALYTIC CONTINUATION | DECAY | MAPS | EIGENFUNCTIONS | FOURIER-TRANSFORMS | PHYSICS, MATHEMATICAL | RESONANCES | EQUATION | Lower bounds | Uncertainty | Fractals | Eigenvectors

SPECTRAL GAPS | LAPLACIAN | ANALYTIC CONTINUATION | DECAY | MAPS | EIGENFUNCTIONS | FOURIER-TRANSFORMS | PHYSICS, MATHEMATICAL | RESONANCES | EQUATION | Lower bounds | Uncertainty | Fractals | Eigenvectors

Journal Article

Communications in mathematical physics, ISSN 1432-0916, 2015, Volume 335, Issue 3, pp. 1445 - 1485

We describe asymptotic behavior of linear waves on Kerr(-de Sitter) black holes and more general Lorentzian manifolds, providing a quantitative analysis of the...

DECAY | SCHWARZSCHILD | STABILITY | PRICES LAW | MANIFOLDS | PHYSICS, MATHEMATICAL | EQUATION | LOCAL ENERGY | Projectors

DECAY | SCHWARZSCHILD | STABILITY | PRICES LAW | MANIFOLDS | PHYSICS, MATHEMATICAL | EQUATION | LOCAL ENERGY | Projectors

Journal Article

Journal of the American Mathematical Society, ISSN 0894-0347, 04/2015, Volume 28, Issue 2, pp. 311 - 381

We prove a Weyl law for scattering resonances in a strip near the real axis when the trapped set is r large and a pinching condition on the normal expansion...

MATHEMATICS | DECAY | BOUNDS | RESOLVENT | SEMICLASSICAL RESONANCES | MANIFOLDS | CONTACT ANOSOV-FLOWS | OPERATORS | BLACK-HOLES | SCATTERING | SURFACES

MATHEMATICS | DECAY | BOUNDS | RESOLVENT | SEMICLASSICAL RESONANCES | MANIFOLDS | CONTACT ANOSOV-FLOWS | OPERATORS | BLACK-HOLES | SCATTERING | SURFACES

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 8/2011, Volume 306, Issue 1, pp. 119 - 163

... and Exponential Energy Decay for the Kerr-de Sitter Black Hole Semyon Dyatlov Department of Mathematics, Evans Hall, University of California, Berkeley, CA 94720, USA. E-mail...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | PERTURBATIONS | RESOLVENT | SPACES | WAVE-EQUATION | MANIFOLDS | PHYSICS, MATHEMATICAL | RESONANCES | LOCAL ENERGY | SCATTERING

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | PERTURBATIONS | RESOLVENT | SPACES | WAVE-EQUATION | MANIFOLDS | PHYSICS, MATHEMATICAL | RESONANCES | LOCAL ENERGY | SCATTERING

Journal Article

Annales Henri Poincaré, ISSN 1424-0661, 2012, Volume 13, Issue 5, pp. 1101 - 1166

... Annales Henri Poincar´ e Asymptotic Distribution of Quasi-Normal Modes for Kerr–de Sitter Black Holes Semyon Dyatlov Abstract. We establish a Bohr–Sommerfeld type...

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 | DECAY | PHYSICS, MULTIDISCIPLINARY | EXPANSIONS | WAVE-EQUATION | PHYSICS, MATHEMATICAL | RESONANCES | OPERATORS | LOCAL ENERGY | SCATTERING | 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 | DECAY | PHYSICS, MULTIDISCIPLINARY | EXPANSIONS | WAVE-EQUATION | PHYSICS, MATHEMATICAL | RESONANCES | OPERATORS | LOCAL ENERGY | SCATTERING | PHYSICS, PARTICLES & FIELDS

Journal Article

Annales de l'Institut Fourier, ISSN 0373-0956, 2016, Volume 66, Issue 1, pp. 55 - 82

We establish a resonance free strip for codimension 2 symplectic normally hyperbolic trapped sets with smooth incoming/outgoing tails. An important application...

Spectral gaps | Black holes | Normally hyperbolic trapping | MATHEMATICS | spectral gaps | BOUNDS | normally hyperbolic trapping | black holes | ENERGY DECAY | LIMITING ABSORPTION PRINCIPLE | RESONANCES

Spectral gaps | Black holes | Normally hyperbolic trapping | MATHEMATICS | spectral gaps | BOUNDS | normally hyperbolic trapping | black holes | ENERGY DECAY | LIMITING ABSORPTION PRINCIPLE | RESONANCES

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 08/2017, Volume 354, Issue 1, pp. 269 - 316

We study eigenvalues of quantum open baker's maps with trapped sets given by linear arithmetic Cantor sets of dimensions . We show that the size of the...

ANOSOV-FLOWS | TRANSFORMATION | DENSITY | BAKERS MAP | ZETA-FUNCTION | WEYL LAWS | DECAY | SPECTRAL SET CONJECTURE | HYPERBOLIC SURFACES | CHAOTIC SCATTERING | PHYSICS, MATHEMATICAL

ANOSOV-FLOWS | TRANSFORMATION | DENSITY | BAKERS MAP | ZETA-FUNCTION | WEYL LAWS | DECAY | SPECTRAL SET CONJECTURE | HYPERBOLIC SURFACES | CHAOTIC SCATTERING | PHYSICS, MATHEMATICAL

Journal Article

Annals of Mathematics, ISSN 0003-486X, 5/2018, Volume 187, Issue 3, pp. 825 - 867

For all convex co-compact hyperbolic surfaces, we prove the existence of an essential spectral gap, that is, a strip beyond the unitarity axis in which the...

Musical intervals | Uncertainty principle | Conformal mapping | Lebesgue measures | Fourier transformations | Fractals | Mathematical surfaces | Mathematical functions | Mathematical congruence | Fractal uncertainty principle | Spectral gap | Scattering resonance | PSEUDO-LAPLACIANS | fractal uncertainty principle | ANALYTIC CONTINUATION | ZETA-FUNCTIONS | COMPLETE SPACES | CHAOTIC SCATTERING | MATHEMATICS | RESOLVENT | scattering resonance | spectral gap | WAVE-EQUATION | RESONANCES | CONSTANT NEGATIVE CURVATURE

Musical intervals | Uncertainty principle | Conformal mapping | Lebesgue measures | Fourier transformations | Fractals | Mathematical surfaces | Mathematical functions | Mathematical congruence | Fractal uncertainty principle | Spectral gap | Scattering resonance | PSEUDO-LAPLACIANS | fractal uncertainty principle | ANALYTIC CONTINUATION | ZETA-FUNCTIONS | COMPLETE SPACES | CHAOTIC SCATTERING | MATHEMATICS | RESOLVENT | scattering resonance | spectral gap | WAVE-EQUATION | RESONANCES | CONSTANT NEGATIVE CURVATURE

Journal Article

Inventiones mathematicae, ISSN 0020-9910, 10/2017, Volume 210, Issue 1, pp. 211 - 229

...Invent. math. (2017) 210:211–229 DOI 10.1007/s00222-017-0727-3 Ruelle zeta function at zero for surfaces Semyon Dyatlov 1 · Maciej Zworski 2 Received: 9...

Mathematics, general | Mathematics | DIFFEOMORPHISMS | MATHEMATICS | SOBOLEV SPACES | MAPS | DYNAMICAL-SYSTEMS | ANALYTIC-TORSION | HYPERBOLIC MANIFOLDS | SPECTRUM | CONTACT ANOSOV-FLOWS | RESONANCES | FREDHOLM DETERMINANTS

Mathematics, general | Mathematics | DIFFEOMORPHISMS | MATHEMATICS | SOBOLEV SPACES | MAPS | DYNAMICAL-SYSTEMS | ANALYTIC-TORSION | HYPERBOLIC MANIFOLDS | SPECTRUM | CONTACT ANOSOV-FLOWS | RESONANCES | FREDHOLM DETERMINANTS

Journal Article

Mathematical Research Letters, ISSN 1073-2780, 2011, Volume 18, Issue 5, pp. 1023 - 1035

We establish an exponential decay estimate for linear waves on the Kerr-de Sitter slowly rotating black hole. Combining the cutoff resolvent estimate of [10]...

MATHEMATICS | WAVE-EQUATION

MATHEMATICS | WAVE-EQUATION

Journal Article

Geometric and Functional Analysis, ISSN 1016-443X, 7/2017, Volume 27, Issue 4, pp. 744 - 771

... Geometric And Functional Analysis FOURIER DIMENSION AND SPECTRAL GAPS FOR HYPERBOLIC SURF ACES Jean Bourgain and Semyon Dyatlov Abstract. We obtain an essential...

Analysis | Mathematics | MATHEMATICS | ANALYTIC CONTINUATION | FLOWS | DECAY | SCATTERING

Analysis | Mathematics | MATHEMATICS | ANALYTIC CONTINUATION | FLOWS | DECAY | SCATTERING

Journal Article

Geometric and Functional Analysis, ISSN 1016-443X, 7/2016, Volume 26, Issue 4, pp. 1011 - 1094

... Geometric And Functional Analysis SPECTRAL GAPS, ADDITIVE ENERGY, AND A FRACT AL UNCER T AINTY PRINCIPLE Semyon Dyatlov and Joshua Zahl Abstract. We obtain an essential...

Analysis | Mathematics | HAUSDORFF DIMENSION | MATHEMATICS | MICROLOCAL ANALYSIS | ZETA-FUNCTIONS | ANALYTIC CONTINUATION | RIEMANN SURFACE | COMPLETE SPACES | ASYMPTOTICALLY HYPERBOLIC MANIFOLDS | KLEINIAN-GROUPS | LAPLACIAN OPERATOR | CONSTANT NEGATIVE CURVATURE

Analysis | Mathematics | HAUSDORFF DIMENSION | MATHEMATICS | MICROLOCAL ANALYSIS | ZETA-FUNCTIONS | ANALYTIC CONTINUATION | RIEMANN SURFACE | COMPLETE SPACES | ASYMPTOTICALLY HYPERBOLIC MANIFOLDS | KLEINIAN-GROUPS | LAPLACIAN OPERATOR | CONSTANT NEGATIVE CURVATURE

Journal Article

Annales Henri Poincaré, ISSN 1424-0637, 11/2016, Volume 17, Issue 11, pp. 3089 - 3146

.../s00023-016-0491-8 Annales Henri Poincar´ e Pollicott–Ruelle Resonances for Open Systems Semyon Dyatlov and Colin Guillarmou Abstract. We deﬁne Pollicott–Ruelle resonances...

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 | ZETA-FUNCTIONS | PHYSICS, MULTIDISCIPLINARY | NEGATIVE CURVATURE | SPACES | AXIOM-A FLOWS | CONTACT ANOSOV-FLOWS | PHYSICS, MATHEMATICAL | EXPANDING MAPS | HYPERBOLIC DIFFEOMORPHISMS | DYNAMICAL-SYSTEMS | SPECTRUM | FREDHOLM DETERMINANTS | 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 | ZETA-FUNCTIONS | PHYSICS, MULTIDISCIPLINARY | NEGATIVE CURVATURE | SPACES | AXIOM-A FLOWS | CONTACT ANOSOV-FLOWS | PHYSICS, MATHEMATICAL | EXPANDING MAPS | HYPERBOLIC DIFFEOMORPHISMS | DYNAMICAL-SYSTEMS | SPECTRUM | FREDHOLM DETERMINANTS | PHYSICS, PARTICLES & FIELDS

Journal Article

International mathematics research notices, ISSN 1073-7928, 02/2020, Volume 2020, Issue 3, pp. 781 - 812

Abstract We show directly that the fractal uncertainty principle of Bourgain–Dyatlov [3] implies that there exists σ > 0 for which the Selberg zeta function...

MATHEMATICS

MATHEMATICS

Journal Article

Applied Mathematics Research eXpress, ISSN 1687-1200, 2016, Volume 2016, Issue 1, pp. 68 - 97

We prove a new polynomial lower bound on the scattering resolvent. For that, we construct a quasimode localized on a trajectory $\gamma$ which is trapped in...

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

ACTA MATHEMATICA, ISSN 0001-5962, 2018, Volume 220, Issue 2, pp. 297 - 339

We show that each limiting semiclassical measure obtained from a sequence of eigenfunctions of the Laplacian on a compact hyperbolic surface is supported on...

SPECTRAL GAPS | LAPLACIAN | MATHEMATICS | BILLIARDS | MANIFOLDS | EIGENFUNCTIONS | FLOW | QUANTUM UNIQUE ERGODICITY | ENTROPY

SPECTRAL GAPS | LAPLACIAN | MATHEMATICS | BILLIARDS | MANIFOLDS | EIGENFUNCTIONS | FLOW | QUANTUM UNIQUE ERGODICITY | ENTROPY

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. In contrast with previous results, we...

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

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