Group Analysis of Non-autonomous Linear Hamiltonians through Differential Galois Theory

Details Group Analysis of Non-autonomous Linear Hamiltonians through Differential Galois Theory Group Analysis of Non-autonomous Linear Hamiltonians through Differential Galois Theory

2010-03-02

arxiv.org/abs/1003.0500v1

Physics

Mathematical Physics

21 pages

Scientific paper

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.

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