Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus

TL;DR

This paper extends the Helmholtz theorem to nondifferentiable Hamiltonian systems using Cresson's quantum calculus, providing a characterization and explicit Hamiltonian formulation for such systems.

Contribution

It introduces a Helmholtz theorem for nondifferentiable systems within Cresson's quantum calculus framework, offering a new way to identify Hamiltonian structures in nondifferentiable dynamics.

Findings

Characterization of nondifferentiable equations with Hamiltonian formulation

Explicit construction of the associated Hamiltonian

Extension of classical Helmholtz theorem to nondifferentiable systems

Abstract

We derive the Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus. Precisely, we give a theorem characterizing nondifferentiable equations, admitting a Hamiltonian formulation. Moreover, in the affirmative case, we give the associated Hamiltonian.