Integrability conditions at order 2 for homogeneous potentials of degree -1

2011/09/26 by Thierry Combot, Combot, Thierry · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #math.DS #nlin.SI

paper · pdf · doi:10.48550/arxiv.1109.5686

30 pages, 2 figures, 10 references

arxiv created 2011/09/26 · arxiv updated 2011/09/27

Abstract

We prove a meromorphic integrability condition at order 2 near a homothetic orbit for a meromorphic homogeneous potential of degree -1, which extend the Morales Ramis conditions of order 1. Conversely, we prove that if this criterion is satisfied, then the Galois group of second order variational equation is abelian and we compute explicitly the Galois group and the Picard-Vessiot extension.

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• Integrability of non-homogeneous Hamiltonian systems with gyroscopic coupling

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