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math.SP2024
Silent Orbits and Cancellations in the Wave Trace
Illya Koval, Amir Vig
This paper shows that the wave trace of a bounded and strictly convex planar domain may be arbitrarily smooth in a neighborhood of some point in the length spectrum. In other words…
math.SP2024
Balian-Bloch Wave Invariants for Nearly Degenerate Orbits
Vadim Kaloshin, Illya Koval, Amir Vig
This paper is part I of a series in which we aim to show that the singular support of the wave trace and the length spectrum of a smooth, strictly convex, and bounded planar billia…
math.DS2024
Billiard tables with analytic Birkhoff normal form are generically Gevrey divergent
Illya Koval
The problem of the existence of an analytic normal form near an equilibrium point of an area-preserving map and analyticity of the associated coordinate change is a classical probl…