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- Nicolas Burq, Semyon Dyatlov, Rachel Ward, Maciej Zworski
- SIAM J. Math. Analysis
- 2012

Using tools from semiclassical analysis, we give weighted Lâˆž estimates for eigenfunctions of strictly convex surfaces of revolution. These estimates give rise to new sampling techniques and provideâ€¦ (More)

- Semyon Dyatlov, M. Zworski
- 2013

The purpose of this paper is to give a short microlocal proof of the meromorphic continuation of the Ruelle zeta function for Câˆž Anosov flows. More general results have been recently proved byâ€¦ (More)

- Semyon Dyatlov
- 2011

We establish a Bohrâ€“Sommerfeld type condition for quasi-normal modes of a slowly rotating Kerrâ€“de Sitter black hole, providing their full asymptotic description in any strip of fixed width. Inâ€¦ (More)

- Semyon Dyatlov, M. Zworski
- 2013

We present dynamical properties of linear waves and null geodesics valid for Kerr and Kerrâ€“de Sitter black holes and their stationary perturbations. The two are intimately linked by the geometricâ€¦ (More)

- Semyon Dyatlov
- 2012

For asymptotically hyperbolic manifolds with hyperbolic trapped sets we prove a fractal upper bound on the number of resonances near the essential spectrum, with power determined by the dimension ofâ€¦ (More)

- KIRIL DATCHEV, Semyon Dyatlov, M. Zworski
- 2012

We give a sharp polynomial bound on the number of Pollicott-Ruelle resonances. These resonances, which are complex numbers in the lower half-plane, appear in expansions of correlations for Anosovâ€¦ (More)

- KIRIL DATCHEV, Semyon Dyatlov, M. Zworski
- 2014

We show how the presence of resonances close to the real axis implies exponential lower bounds on the norm of the cut-off resolvent on the real axis. In this note we establish exponential lowerâ€¦ (More)

- Semyon Dyatlov, M. Zworski
- 2014

Pollicottâ€“Ruelle resonances for chaotic flows are the characteristic frequencies of correlations. They are typically defined as eigenvalues of the generator of the flow acting on specially designedâ€¦ (More)

- Semyon Dyatlov, M. Zworski
- 2017

We show that the Ruelle zeta function for a negatively curved oriented surface vanishes at zero to the order given by the absolute value of the Euler characteristic. This result was previously knownâ€¦ (More)

- Semyon Dyatlov
- 2016

We give an overview of the quantum ergodicity result. 1. Quantum ergodicity in the physical space 1.1. Concentration of eigenfunctions. First, let us consider the case when M âŠ‚ R is a bounded domainâ€¦ (More)