Kahan–Hirota–Kimura maps preserving original cubic Hamiltonians

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation Pub Date : 2025-05-24 DOI:10.1016/j.matcom.2025.05.002

Víctor Mañosa , Chara Pantazi

引用次数: 0

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

R^{2}

and

R^{4}

, extending to a family of fields in

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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Kahan-Hirota-Kimura地图保留了原始的三次哈密顿量

研究了一类三次哈密顿向量场，其相关的Kahan-Hirota-Kimura （KHK）映射保持了原始哈密顿函数。我们的分析主要集中在R2和R4中的这些字段，并扩展到R6中的一系列字段。此外，我们研究了这些场的各种性质，包括特定类型的附加第一积分的存在性，它们作为相应KHK映射的Lie对称性的作用，以及这些映射的辛性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematics and Computers in Simulation 数学-计算机：跨学科应用

CiteScore

8.90

自引率

4.30%

发文量

335

审稿时长

54 days

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