Kahan–Hirota–Kimura maps preserving original cubic Hamiltonians
Copyright policy )Kahan–Hirota–Kimura maps preserving original cubic Hamiltonians
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 $\mathbb{R}^2$ and $\mathbb{R}^4$, extending to a family of fields in $\mathbb{R}^6$. 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.
32 pages, 1 Figure
Àrees temàtiques de la UPC::Matemàtiques i estadística, Nonlinear Sciences - Exactly Solvable and Integrable Systems, 37J35, 37J11, 37J70, 37M15, 14E05, FOS: Physical sciences, Dynamical Systems (math.DS), Kahan-Hirota-Kimura discretization, Lie Symmetries, Hamiltonian vector fields, Symplectic maps, FOS: Mathematics, Mathematics - Dynamical Systems, Exactly Solvable and Integrable Systems (nlin.SI), Integrable maps, Kahan–Hirota–Kimura discretization
Àrees temàtiques de la UPC::Matemàtiques i estadística, Nonlinear Sciences - Exactly Solvable and Integrable Systems, 37J35, 37J11, 37J70, 37M15, 14E05, FOS: Physical sciences, Dynamical Systems (math.DS), Kahan-Hirota-Kimura discretization, Lie Symmetries, Hamiltonian vector fields, Symplectic maps, FOS: Mathematics, Mathematics - Dynamical Systems, Exactly Solvable and Integrable Systems (nlin.SI), Integrable maps, Kahan–Hirota–Kimura discretization
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