6 citations · 6 across the 7 of their papers we have counts for
7 papers
Rigidity of Mather's -function on a KAM set for analytic billiards-like maps and unique quasi-analytic continuation
Corentin Fierobe, Vadim Kaloshin, Frank Trujillo
In his seminal paper, Kac famously asked whether "one can hear the shape of a drum" - that is whether the isometry class of a bounded domain in a Euclidean space is uniquely determ…
Normal distribution of Lyapunov exponents of periodic orbits for expanding circle maps
Kostiantyn Drach, Zhi Fu, Vadim Kaloshin +2
For a smooth expanding circle map, we show that the empirical distribution of Lyapunov exponents of periodic points of any fixed period is close to normal, with an error that decre…
Unmarked spectral rigidity of expanding circle maps
Kostiantyn Drach, Vadim Kaloshin
For a smooth expanding map of the circle, its (unmarked) length spectrum is defined as the set of logarithms of multipliers of periodic orbits of . This spectrum is analogou…
A billiard table close to an ellipse is deformationally spectrally rigid among dihedrally symmetric domains
Corentin Fierobe, Vadim Kaloshin, Alfonso Sorrentino
We prove that a a strongly convex planar domain (Birkhoff table) with dihedral symmetry, which is sufficiently close in a finitely smooth topology to an ellipse, is deformationally…
Spectral rigidity of two-dimensional Liouville tori
Joscha Henheik, Vadim Kaloshin, Yunzhe Li +1
It is a folklore conjecture that Liouville metrics are the only Riemannian metrics with integrable geodesic flow on the two-dimensional torus. In this paper, we study Laplace-isosp…
Kuznecov remainders and generic metrics
Vadim Kaloshin, Emmett L. Wyman, Yakun Xi
We obtain improved remainder estimates in the Kuznecov sum formula for period integrals of Laplace eigenfunctions on a Riemannian manifold . Building upon the two-term asymptoti…
Coexistence of periodic-2 and periodic-3 caustics for nearly circular analytic billiard maps
Vadim Kaloshin, Jianlu Zhang
For symmetrically analytic deformation of the circle (with certain Fourier decaying rate), the necessary condition for the corresponding billiard map to keep the coexistence of per…