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Kahan-Hirota-Kimura maps preserving original cubic hamiltonians
- Publication Year :
- 2024
-
Abstract
- In this work we investigate the set of cubic Hamiltonian vector fields for which their associated Kahan-Hirota-Kimura maps preserve the original Hamiltonian function. We analyze these fields in $\mathbb{R}^2$ and $\mathbb{R}^4$. We also study a family of fields in $\mathbb{R}^6$. Additionally, we explore several properties like the existence of additional first integrals of specific type, the possibility that the initial Hamiltonian vector field is a Lie symmetry of the corresponding map, or the symplecticity of the considered maps.<br />Comment: 30 pages, 1 Figure
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2405.01321
- Document Type :
- Working Paper