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arXiv · 2405.01321

Kahan-Hirota-Kimura maps preserving original cubic hamiltonians

Víctor Mañosa·Chara Pantazi
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Abstract

We study the class of cubic Hamiltonian vector fields whose associated Kahan-Hirota-Kimura (KHK) maps preserve the original Hamiltonian function. Our analysis focuses on these fields in $\mathbb{R}^2$ and $\mathbb{R}^4$, extending to a family of fields in $\mathbb{R}^6$. Additionally, we investigate various properties of these fields, including the existence of additional first integrals of a specific type, their role as Lie symmetries of the corresponding KHK map, and the symplecticity of these maps.

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Víctor Mañosa, Chara Pantazi. 2024-05-02. Kahan-Hirota-Kimura maps preserving original cubic hamiltonians. https://doi.org/10.1016/j.matcom.2025.05.002

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