89 citations · 1.1k across the 43 of their papers we have counts for
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math.CA2016★ 89 cited
Spectral gaps without the pressure condition
Jean Bourgain, Semyon Dyatlov
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 Selberg zeta function has…
math.SP2016★ 29 cited
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…
math.DS2016★ 54 cited
Ruelle zeta function at zero for surfaces
Semyon Dyatlov, Maciej Zworski
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 wa…