Third order integrability conditions for homogeneous potentials of degree -1

Details Third order integrability conditions for homogeneous potentials of degree -1 Third order integrability conditions for homogeneous potentials of degree -1

2011-11-25

arxiv.org/abs/1111.5971v1

Mathematics

Dynamical Systems

30 pages, 2 figures

Scientific paper

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 directly except for families of potentials whose eigenvalues are bounded. To address this issue, we use holonomic and asymptotic computations with error control of this criterion and apply it to the potential of the form V(r,\theta)=r^{-1} h(\exp(i\theta)) with h a polynomial of degree less than 3. We find then all meromorphically integrable potentials of this form.

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