Michael RUDNEV

Dept. of Mathematics /C 1200
UT at Austin
Austin, TX 78712
USA
mru@math.utexas.edu

A geometric method for the splitting of separatrices

Abstract : A new method to study the splitting of separatrices in near-integrable Hamiltonian systems is presented, which allows to prove exponentially small upper bounds for the splitting for a generic Hamiltonian with two time scales.

The issues of obtaining the lower bounds in exponentially small case are addressed, in particular how one can come up with exact asymptotics in a model problem with three degrees of freedom.