Poisson systems as the natural framework for additional first integrals via Darboux invariant hypersurfaces

DOI10.1016/j.bulsci.2011.09.005zbMath1314.37043arXiv1910.08749OpenAlexW2047699864MaRDI QIDQ390825

Isaac A. García, Benito Hernández-Bermejo

Publication date: 9 January 2014

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.08749

zbMATH Keywords

Hamiltonian systemfirst integralPoisson systemDarboux polynomialCasimir invariantsDarboux canonical form

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

Related Items (2)

Inverse Jacobi multiplier as a link between conservative systems and Poisson structures ⋮ Periodic orbits in analytically perturbed Poisson systems

Cites Work

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• First integrals and Darboux polynomials of natural polynomial Hamiltonian systems
• Characterization, global analysis and integrability of a family of Poisson structures
• Generalization of solutions of the Jacobi PDEs associated to time reparametrizations of Poisson systems
• Perturbed Euler top and bifurcation of limit cycles on invariant Casimir surfaces
• Darboux polynomials and first integrals of natural polynomial Hamiltonian systems

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