Kahan–Hirota–Kimura maps preserving original cubic Hamiltonians

Víctor Mañosa and Chara Pantazi

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 238, issue C, 240-254

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 R2 and R4, extending to a family of fields in R6. 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.

Keywords: Integrable maps; Kahan–Hirota–Kimura discretization; Lie Symmetries; Symplectic maps; Hamiltonian vector fields (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:238:y:2025:i:c:p:240-254

DOI: 10.1016/j.matcom.2025.05.002

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