89 citations · 1.1k across the 43 of their papers we have counts for
6 papers · 1 filter
Resonances for open quantum maps and a fractal uncertainty principle
Semyon Dyatlov, Long Jin
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 spectral gap is…
Improved fractal Weyl bounds for hyperbolic manifolds
Semyon Dyatlov, David Borthwick, Tobias Weich
We give a new fractal Weyl upper bound for resonances of convex co-compact hyperbolic manifolds in terms of the dimension of the manifold and the dimension of its limit set…
Spectral gaps, additive energy, and a fractal uncertainty principle
Semyon Dyatlov, Joshua Zahl
We obtain an essential spectral gap for -dimensional convex co-compact hyperbolic manifolds with the dimension of the limit set close to . The size of the gap is ex…
Sharp polynomial bounds on the number of Pollicott-Ruelle resonances
Kiril Datchev, Semyon Dyatlov, Maciej Zworski
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 correlat…
Scattering phase asymptotics with fractal remainders
Semyon Dyatlov, Colin Guillarmou
For a Riemannian manifold which is isometric to the Euclidean space outside of a compact set, and whose trapped set has Liouville measure zero, we prove Weyl type asymptoti…
Microlocal limits of Eisenstein functions away from the unitarity axis
Semyon Dyatlov
We consider a surface M with constant curvature cusp ends and its Eisenstein functions E_j(λ). These are the plane waves associated to the j-th cusp and the spectral parameter λ, (…