Kahan-Hirota-Kimura maps preserving original cubic hamiltonians

2024/05/02 by Vı́ctor Mañosa, Mañosa, Víctor, Chara Pantazi +1
Mathematics · #14E05 #37J11 #37J35 #37J70 #37M15 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2405.01321

openalex publication_date 2024/05/02 · openalex created_date 2024/05/05 · openalex updated_date 2026/07/28

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.

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