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[ math ] mathematics [math] (1) 1
[ math.math-ap ] mathematics [math]/analysis of pdes [math.ap] (1) 1
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[math.math-ap]mathematics [math]/analysis of pdes [math.ap] (1) 1
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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
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
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
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
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
Journal Article
Annales Henri Poincaré, ISSN 1424-0661, 2012, Volume 13, Issue 5, pp. 1101 - 1166
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
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
Journal Article
Annals of Mathematics, ISSN 0003-486X, 5/2018, Volume 187, Issue 3, pp. 825 - 867
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
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
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
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
Journal Article
Annales Henri Poincaré, ISSN 1424-0637, 11/2016, Volume 17, Issue 11, pp. 3089 - 3146
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
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
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
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
Journal Article
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