2026-04-18T03:39:06Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/4078382025-07-17T11:12:27Zcom_2072_1033col_2072_452950

Kahan-Hirota-Kimura maps preserving original cubic hamiltonians Mañosa Fernández, Víctor Pantazi, Chara Universitat Politècnica de Catalunya. Departament de Matemàtiques Universitat Politècnica de Catalunya. UPCDS - Grup de Sistemes Dinàmics de la UPC Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals 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 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. "The authors are supported by the Ministry of Science and Innovation–State Research Agency of the Spanish Government through grant PID2022-136613NB-I00. They also acknowledge the 2021 SGR 01039 consolidated research groups recognition from Ag` encia de Gesti´ o d’Ajuts Universitaris i de Recerca, Generalitat de Catalunya" Preprint 2024-05-02 External research report Mañosa, V.; Pantazi, C. Kahan-Hirota-Kimura maps preserving original cubic hamiltonians. 2024. https://arxiv.org/abs/2405.01321 https://hdl.handle.net/2117/407838 eng arXiv:2405.01321 [nlin.SI] info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-136613NB-I00/ES/SISTEMAS DINAMICOS CONTINUOS Y DISCRETOS: BIFURCACIONES, ORBITAS PERIODICAS, INTEGRABILIDAD Y APLICACIONES/ http://creativecommons.org/licenses/by/4.0/ Open Access Attribution 4.0 International 31 p. application/pdf