Integrable systems in cosymplectic geometry

TL;DR

This paper extends the concepts of integrability and action-angle variables from symplectic to cosymplectic manifolds, motivated by time-dependent Hamiltonian dynamics, and proves a variant of non-commutative integrability.

Contribution

It introduces a new framework for integrability in cosymplectic geometry, including a construction of action-angle variables and a proof of non-commutative integrability for key vector fields.

Findings

Established a variant of non-commutative integrability on cosymplectic manifolds

Constructed cosymplectic action-angle variables

Extended Hamiltonian integrability concepts to time-dependent systems

Abstract

Motivated by the time-dependent Hamiltonian dynamics, we extend the notion of Arnold-Liouville and noncommutative integrability of Hamiltonian systems on symplectic manifolds to that on cosymplectic manifolds. We prove a variant of the non-commutative integrability for evaluation and Reeb vector fields on cosymplectic manifolds and provide a construction of cosymplectic action-angle variables.