Slow drift in a slow-fast Hamiltonian system
We study the drift of slow variables induced by chaotic
motion of the fast variables in a Hamiltonian system with two
different time-scales. We assume that the fast system with
frozen slow variables has a pair of hyperbolic periodic orbits
connected by two transversal heteroclinic trajectories.
We define the class of accessible paths and
show every accessible path is shadowed by
the slow component of a trajectory of the full system.
For any periodic trajectory of the fast subsystem with the frozen slow variables
we define an action. For a family of periodic orbits, the action is a scalar function
of the slow variables and can itself be considered as a Hamiltonian function.
An accessible path consists of segments of the corresponding trajectories.