Homoclinic orbits to invariant tori in nearly integrable Hamiltonian systems

Lev Lerman
Dept. of Differential Equations and Math. Analysis
University of Nizhny Novgorod, Russia

Consider a Hamiltonian system with three degrees of freedom that is a perturbation of integrable one with a homoclinic orbit to a elliptic-hyperbolic equilibrium. I will discuss conditions when this perturbed system has homoclinic orbits to invariant tori in the center manifold of the equilibrium. It is proved that the number of such orbits can range generically from 4 to 16 depending upon the perturbation.

Homoclinic orbits to invariant tori in nearly integrable Hamiltonian systems

Lev Lerman Dept. of Differential Equations and Math. Analysis University of Nizhny Novgorod, Russia

Lev Lerman
Dept. of Differential Equations and Math. Analysis
University of Nizhny Novgorod, Russia