Structure preserving integration of 3D dissipative bi-Hamiltonian/Nambu systems

2026/06/01 by Bülent Karasözen, Murat Uzunca · 1 voice
Physics and Astronomy · #nlin.CD

paper · pdf

Abstract

A structure-preserving splitting integrator is developed for 3D dissipative bi-Hamiltonian/Nambu systems. The integrator uses Strang splitting for conservative and dissipative parts. For Nambu systems, the divergence-free, conservative part is integrated using the energy/volume-preserving Kahan's method, and the dissipative part is integrated by the forward and backward Euler methods. For dissipative bi-Hamiltonian systems, the conservative part is integrated with the energy-preserving average vector field (AVF) method. In both cases, the Hamiltonians of the conservative parts are preserved in the Lorenz, Chen, and Rabinovich systems. The periodic and chaotic solutions are computed accurately by the conservative-dissipative Strang splitting approach.

Citations

• On novel Hamiltonian descriptions of some three-dimensional non-conservative systems
• Splitting Methods for differential equations
• Linearly implicit exponential integrators for damped Hamiltonian PDEs
• Using aromas to search for preserved measures and integrals in Kahan's method
• Geometric and integrability properties of Kahan's method
• Structure-preserving integrators for dissipative systems based on reversible-irreversible splitting
• On Integrals, Hamiltonian and Metriplectic Formulations of 3D Polynomial Systems
• Phase Space Geometry and Chaotic Attractors in Dissipative Nambu Mechanics
• Strange attractors in dissipative Nambu mechanics: classical and quantum aspects
• Splitting methods
• YET ANOTHER CHAOTIC ATTRACTOR
• On foundation of the generalized Nambu mechanics
• Deterministic Nonperiodic Flow
• Generalized Hamiltonian Dynamics

Discussions

• B\"ulent Karas\"ozen, Murat Uzunca: Structure preserving integration of 3D dissipative bi-Hamiltonian/Nambu systems https://arxiv.org/abs/2606.02827 https://arxiv.org/pdf/2606.02827 https://arxiv.org/ [bsky, 0 points, 0 comments]

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