Kahan–Hirota–Kimura maps preserving original cubic Hamiltonians

Mañosa Fernández, Víctor; Pantazi, Chara

doi:10.1016/j.matcom.2025.05.002

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Mañosa Fernández, Víctor

Pantazi, Chara

Document typeArticle

Defense date2025-12

PublisherElsevier

Rights accessOpen Access

Attribution-NonCommercial-NoDerivs 4.0 International

This work is protected by the corresponding intellectual and industrial property rights. Except where otherwise noted, its contents are licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 4.0 International

ProjectSISTEMAS DINAMICOS CONTINUOS Y DISCRETOS: BIFURCACIONES, ORBITAS PERIODICAS, INTEGRABILIDAD Y APLICACIONES (AEI-PID2022-136613NB-I00)

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.

Description

© 2025 The Authors. Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation (IMACS). This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

CitationMañosa, V.; Pantazi, C. Kahan–Hirota–Kimura maps preserving original cubic Hamiltonians. "Mathematics and computers in simulation", Desembre 2025, vol. 238, p. 240-254.

URIhttp://hdl.handle.net/2117/432833

DOI10.1016/j.matcom.2025.05.002

ISSN0378-4754

Publisher versionhttps://www.sciencedirect.com/science/article/pii/S0378475425001855

Other identifiershttps://arxiv.org/abs/2405.01321

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