The Hamilton--Jacobi theory for contact Hamiltonian systems

TL;DR

This paper develops a Hamilton-Jacobi theory tailored for contact Hamiltonian systems, exploring different formulations, their relations, and providing illustrative examples to enhance understanding of these systems.

Contribution

It introduces a new Hamilton-Jacobi framework for contact Hamiltonian systems and analyzes its relation to symplectification, offering a comprehensive approach.

Findings

Multiple forms of Hamilton-Jacobi equations for contact systems

Relations established between contact and symplectified formulations

Examples demonstrating the application of the theory

Abstract

The aim of this paper is to develop a Hamilton--Jacobi theory for contact Hamiltonian systems. We find several forms for a suitable Hamilton-Jacobi equation accordingly to the Hamiltonian and the evolution vector fields for a given Hamiltonian function. We also analyze the corresponding formulation on the symplectification of the contact Hamiltonian system, and establish the relations between these two approaches. In the last section, some examples are discussed.