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Kahan–Hirota–Kimura maps preserving original cubic Hamiltonians

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  • Mañosa, Víctor
  • Pantazi, Chara

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.

Suggested Citation

  • Mañosa, Víctor & Pantazi, Chara, 2025. "Kahan–Hirota–Kimura maps preserving original cubic Hamiltonians," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 238(C), pages 240-254.
    • Handle: RePEc:eee:matcom:v:238:y:2025:i:c:p:240-254
    DOI: 10.1016/j.matcom.2025.05.002
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    References listed on IDEAS

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    1. Haggar, F.A. & Byrnes, G.B. & Quispel, G.R.W. & Capel, H.W., 1996. "k-integrals and k-Lie symmetries in discrete dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 233(1), pages 379-394.
    2. Freddy Dumortier & Jaume Llibre & Joan C. Artés, 2006. "Qualitative Theory of Planar Differential Systems," Springer Books, Springer, number 978-3-540-32902-2, January.
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