Global angle-action variables for Duffing system

TL;DR

This paper introduces a novel method for constructing global action-angle variables in Hamiltonian systems, demonstrated on the Duffing system, enabling better analysis of complex dynamics beyond local perturbation approaches.

Contribution

The paper presents a new topological covering method for global action-angle variable construction, extending the applicability to complex Hamiltonian systems like the Duffing oscillator.

Findings

Successfully constructed global action-angle variables for the Duffing system

Demonstrated the method's effectiveness in analyzing chaotic dynamics

Provides a framework for applying global variables to other Hamiltonian systems

Abstract

The classical representation of Hamiltonian systems in terms of action-angle variables are defined for simply connected domains such as an interior of a homoclinic orbit. On this basis methods of (local) perturbations leading, in particular, to chaotic systems have been studied in literature. We are describing a new method for constructing global action-angle variables and successive perturbations based on a topological covering of the phase space. The method is demonstrated for representative example of the Duffing system.