Sergey V. BOLOTIN

Department of Mathematics and Mechanics, Moscow State University.
Vorob'evy Gory, Moscow 119899, Russia
bolotin@mech.math.msu.su
 

Diffusion trajectories with unbounded energy for time periodic Hamiltonian systems.

Abstract: The result of Mather on the existence of trajectories with unbounded energy for time periodic Hamiltonian systems on a torus is generalized to a class of Hamiltonian systems possessing a hyperbolic invariant torus. Instead of the variational methods of Mather, a geometrical approach based on KAM theory and the Poincare-Melnikov method is used. This makes it possible to study a more general Hamiltonian systems, but requires additional regularity assumptions on the Hamiltonian.