Kahan-Hirota-Kimura maps preserving original cubic hamiltonians
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 R2 and R4. We also study a family of fields in R6. Additionally, we explore several properties like the ex...
| Autores: | , |
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/407838 |
| Acceso en línea: | https://hdl.handle.net/2117/407838 |
| Access Level: | acceso abierto |
| Palabra clave: | Differentiable dynamical systems Kahan-Hirota-Kimura discretization Hamiltonian vector fields Integrable maps Lie Symmetries Symplectic maps Sistemes dinàmics diferenciables Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Classificació AMS::37 Dynamical systems and ergodic theory::37M Approximation methods and numerical treatment of dynamical systems Classificació AMS::14 Algebraic geometry::14E Birational geometry Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals |
| Sumario: | 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 R2 and R4. We also study a family of fields in R6. 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. |
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