Title: Drift in the slow variables of slow-fast Hamiltonian systems
Abstract:
I will present joint work with Vassili Gelfreich.
In this talk we will study drift in the slow dynamics of an a-priori
unstable slow-fast Hamiltonian system. We consider a Hamiltonian system
with Hamiltonian H(x,y,u,v) and symplectic form dx^dy+(1/epsilon)du^dv
where epsilon is a small parameter. We assume that the unperturbed fast
dynamics has smooth families of saddle periodic orbits where every pair of
periodic orbits are connected by transverse heteroclinic orbits. On each
periodic family we define an action J, which can be considered as a
Hamiltonian function. Each Hamiltonian J (which depends on the particular
periodic orbit) generates some slow dynamics. We show that for any path
composed of a finite sequence of trajectories generated by the Hamilonians
J there is a trajectory of the full system whose slow component shadows
that path.