3 papers
math.DS2026
Isoenergetic degeneracy generically creates meandering invariant tori
Vadim Kaloshin, Illya Koval, Yi Pan
Consider the set of isoenergetically degenerate integrable Hamiltonians with two degrees of freedom. We show that a cusp-generic perturbation of a generic Hamiltonian in this set g…
math.CO2024
Exponentially many graphs are determined by their spectrum
Illya Koval, Matthew Kwan
As a discrete analogue of Kac's celebrated question on "hearing the shape of a drum", and towards a practical graph isomorphism test, it is of interest to understand which graphs a…
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…