Uniqueness of contact Hamiltonians of topological strictly contact isotopies

TL;DR

This paper establishes a bijective correspondence between the limits of smooth strictly contact isotopies and their Hamiltonians in the context of regular contact forms, linking geometric isotopies with their analytical Hamiltonian limits.

Contribution

It proves a new correspondence between $C^0$ limits of contact isotopies and Hamiltonians, enhancing understanding of contact dynamics and Hamiltonian uniqueness.

Findings

Establishes a bijective correspondence for regular contact forms.

Connects $C^0$ limits of isotopies with Hamiltonian limits.

Provides a framework for analyzing contact isotopies via Hamiltonians.

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.