On Locally Conformally Cosymplectic Hamiltonian Dynamics and Hamilton-Jacobi Theory

TL;DR

This paper explores the geometric structure of locally conformally cosymplectic manifolds and develops a Hamilton-Jacobi theory within this framework, addressing the challenge of globalizing local Hamiltonian dynamics.

Contribution

It introduces a geometric Hamilton-Jacobi theory on locally conformally cosymplectic manifolds and investigates the globalization of local Hamiltonian dynamics in this setting.

Findings

Developed a Hamilton-Jacobi theory for LCC manifolds

Analyzed the geometry of locally conformally cosymplectic manifolds

Addressed the globalization problem of local Hamiltonian dynamics

Abstract

Cosymplectic geometry has been proven to be a very useful geometric background to describe time-dependent Hamiltonian dynamics. In this work, we address the globalization problem of locally cosymplectic Hamiltonian dynamics that failed to be globally defined. We investigate both the geometry of locally conformally cosymplectic (abbreviated as LCC) manifolds and the Hamiltonian dynamics constructed on such LCC manifolds. Further, we provide a geometric Hamilton-Jacobi theory on this geometric framework.