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arXiv · 2601.20799

Jacobi Hamiltonian Integrators: construction and applications

Adérito Araújo·Gonçalo Inocêncio Oliveira·João Nuno Mestre
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Abstract

We propose a systematic framework for constructing geometric integrators for Hamiltonian systems on Jacobi manifolds. By combining Poissonization of Jacobi structures with homogeneous symplectic bi-realizations, Jacobi dynamics are lifted to homogeneous Poisson Hamiltonian systems, enabling the construction of structure-preserving Jacobi Hamiltonian integrators. The resulting schemes are constructed explicitly and applied to a range of examples, including contact Hamiltonian systems and classical models. Numerical experiments highlight their qualitative advantages over standard integrators, including better preservation of geometric structure and improved long-time behavior.

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Adérito Araújo, Gonçalo Inocêncio Oliveira, João Nuno Mestre. 2026-01-28. Jacobi Hamiltonian Integrators: construction and applications. https://arxiv.org/abs/2601.20799

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