  We investigate the relation between the phase space structure of Hamiltonian
and non-Hamiltonian deterministic thermostats. We show that phase space
structures governing reaction dynamics in Hamiltonian systems map to the same
type of phase space structures for the non-Hamiltonian isokinetic equations of
motion for the thermostatted Hamiltonian. Our results establish a framework for
analyzing thermostat dynamics using concepts and methods developed in reaction
rate theory.
