Lobachevskii Journal of Mathematics

, Volume 31, Issue 2, pp 157–173 | Cite as

Group analysis of non-autonomous linear Hamiltonians through differential Galois theory

  • D. Blázquez-SanzEmail author
  • S. A. Carrillo Torres


In this paper we introduce a notion of integrability in the non autonomous sense. For the cases of 1 + 1/2 degrees of freedom and quadratic homogeneous Hamiltonians of 2 + 1/2 degrees of freedom we prove that this notion is equivalent to the classical complete integrability of the system in the extended phase space. For the case of quadratic homogeneous Hamiltonians of 2 + 1/2 degrees of freedom we also give a reciprocal of the Morales-Ramis result. We classify those systems by terms of symplectic change of frames involving algebraic functions of time, and give their canonical forms.

Key words and phrases

Hamiltonian Systems Integrability Differential Galois Theory 


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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Instituto de Matemáticas y sus Aplicaciones (IMA)Universidad Sergio ArboledaBogotáColombia
  2. 2.Facultad de CienciasDepartamento de Matemáticas Universidad Nacional de ColombiaBogotáColombia

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