27 citations · 62 across the 20 of their papers we have counts for
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Non integrability of the n body problem with non zero angular momentum
Thierry Combot
We prove an integrability criterion and a partial integrability criterion for homogeneous potentials of degree -1 which are invariant by rotation. We then apply it to the proof of…
Third order integrability conditions for homogeneous potentials of degree -1
Thierry Combot, Christoph Koutschan
We prove an integrability criterion of order 3 for a homogeneous potential of degree -1 in the plane. Still, this criterion depends on some integer and it is impossible to apply it…
Integrable homogeneous potentials of degree in the plane with small eigenvalues
Thierry Combot
We give a complete classification of meromorphically integrable homogeneous potentials of degree which are real analytic on . In the more gene…
Integrability conditions at order 2 for homogeneous potentials of degree -1
Thierry Combot
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…