Journal of Symplectic Geometry
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 C0 -rigidity of smooth contact Hamiltonians, a transformation law for topological contact dynamical systems, and C0 -rigidity of the geodesic flows of Riemannian manifolds.
Müller, Stefan, Peter Spaeth.
"Topological Contact Dynamics III: Uniqueness of the Topological Hamiltonian and C0-Rigidity of the Geodesic Flow."
Journal of Symplectic Geometry, 14 (1): 1-29.