Electron. J. Diff. Equ., Vol. 2012 (2012), No. 108, pp. 1-6.

Polynomial and rational integrability of polynomial Hamiltonian systems

Jaume Llibre, Cristina Stoica, Claudia Valls

Within the class of canonical polynomial Hamiltonian systems anti-symmetric under phase-space involutions, we generalize some results on the existence of Darboux polynomial and rational first integrals for "kinetic plus potential" systems to general systems.

Submitted January 26, 2012. Published June 26, 2012.
Math Subject Classifications: 37J35, 37K10.
Key Words: Polynomial Hamiltonian systems; polynomial first integrals; rational first integrals; Darboux polynomial.

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Jaume Llibre
Departament de Matematiques
Universitat Autònoma de Barcelona
08193 Bellaterra, Barcelona
Catalonia, Spain
email: jllibre@mat.uab.cat
  Cristina Stoica
Department of Mathematics, Wilfrid Laurier University
Waterloo, N2L 3C5, Ontario, Canada
email: cstoica@wlu.ca
  Cláudia Valls
Departamento de Matemática, Instituto Superior Técnico
Universidade Técnica de Lisboa
Av. Rovisco Pais, 1049--001, Lisboa, Portugal
email: cvalls@math.ist.utl.pt

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