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

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

2011-09-26

arxiv.org/abs/1109.5686v1

Mathematics

Dynamical Systems

30 pages, 2 figures, 10 references

Scientific paper

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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