Formulation of Stochastic Contact Hamiltonian Systems

TL;DR

This paper introduces a stochastic extension of contact Hamiltonian systems, demonstrating that their phase flows preserve contact structures and identifying conditions for their complete integrability, thus providing a new framework for their analysis.

Contribution

It formulates a stochastic version of contact Hamiltonian systems and establishes conditions for their complete integrability, advancing the theoretical understanding of stochastic contact dynamics.

Findings

Phase flows preserve contact structures

Provided a sufficient condition for complete integrability

Established a framework for stochastic contact Hamiltonian systems

Abstract

In this work we devise a stochastic version of contact Hamiltonian systems, and show that the phase flows of these systems preserve contact structures. Moreover, we provide a sufficient condition under which these stochastic contact Hamiltonian systems are completely integrable. This establishes an appropriate framework for investigating stochastic contact Hamiltonian systems.