Integration on q-Cosymplectic Manifolds

2025/09/20 by Leok, M., Sardón, C., Zhao, X. · 1 citation
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2509.16587

Abstract

This paper presents a unified framework for studying dynamics and integration on q-cosymplectic manifolds. After outlining the geometric foundations of q-cosymplectic structures, we derive new results concerning integrable systems and the characterization of Liouville coordinates, and further investigate the Lie integrability of q-evolution systems in this setting. We then develop a Hamilton--Jacobi theory tailored to multi-time Hamiltonian systems, both from an intrinsic geometric perspective and via symplectification techniques. To illustrate the applicability of the framework, we construct a q-cosymplectic Hamiltonian model for an extended FitzHugh-Nagumo system, providing a biologically relevant example involving three distinct temporal scales.

Citations

• q-Cosymplectic Geometry, Integrability and Reduction
• A geometric description of some thermodynamical systems
• A geometric description of some thermodynamical systems
• Bifurcations and canards in the FitzHugh-Nagumo system: a tutorial in fast-slow dynamics
• Spike-Adding Mechanisms in a Three-Timescale System: Insights from the FitzHugh-Nagumo Model with Periodic Forcing
• On the splitting of weak nearly cosymplectic manifolds
• Contact foliations and generalised Weinstein conjectures
• Implicit Contact Dynamics and Hamilton-Jacobi Theory
• Generalized k-contact structures
• A conceptual approach to the problem of action-angle variables
• Hamilton-Jacobi theory, Symmetries and Coisotropic Reduction

Cited by

• On the splitting of weak nearly \cal C-manifolds
• Weak Nearly \mathcal S- and Weak Nearly \mathcal C- Manifolds

Related

• q-Cosymplectic Geometry, Integrability and Reduction
• A geometric approach to solve time dependent and dissipative Hamiltonian systems
• Coisotropic embeddings of precosymplectic manifolds
• Symplectic manifolds and Hamiltonian dynamical systems
• Polysymplectic Hamiltonian Field Theory