Uniqueness of contact Hamiltonians of topological strictly contact isotopies

Abstract

We prove that for regular contact forms there exists a bijective correspondence between the $C^0$ limits of sequences of smooth strictly contact isotopies and the limits with respect to the contact distance of their corresponding Hamiltonians.

arXiv commentLemma 4.3 from version [v3] is incorrect. We kindly thank an anonymous referee for finding this error. In the new version [v4] the results have been updated accordingly. To appear in Complex Analysis and Dynamical Systems VII, Contemp. Math., 699, Amer. Math. Soc., Providence, RI, 2017