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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.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…