Kuznetsov I.V. Plotnikov P.I.
Kolmogorov's theorem for low-dimensional tori of Hamiltonian systems
Reporter: Kuznetsov I.V.
The problem of persistence of low-dimensional invariant tori under
small perturbation of integrable hamiltonian systems is considered.
The existence of one-to-one correspondence between weak hyperbolic
invariant tori of a perturbed system and critical points of a smooth
function of two real variables is established. It is proved that if
the unperturbed Hamiltonian has a saddle point, then a
weak-hyperbolic torus persists under an arbitrary analytic
perturbation.
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