  We prove that a topological contact isotopy uniquely defines a topological
contact Hamiltonian. Combined with previous results from [MS11], this
generalizes the classical one-to-one correspondence between smooth contact
isotopies and their generating smooth contact Hamiltonians and conformal
factors to the group of topological contact dynamical systems. Applications of
this generalized correspondence include C^0-rigidity of smooth contact
Hamiltonians, a transformation law for topological contact dynamical systems,
and C^0-rigidity of the geodesic flows of Riemannian manifolds.
