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.