Finiteness of integrable $n$-dimensional homogeneous polynomial potentials

Details Finiteness of integrable $n$-dimensional homogeneous polynomial potentials Finiteness of integrable $n$-dimensional homogeneous polynomial potentials

2007-01-30

arxiv.org/abs/nlin/0701059v1

Phys Lett A. vol 369, no 3, 180--187 (2007)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

10.1016/j.physleta.2007.04.077

We consider natural Hamiltonian systems of $n>1$ degrees of freedom with
polynomial homogeneous potentials of degree $k$. We show that under a
genericity assumption, for a fixed $k$, at most only a finite number of such
systems is integrable. We also explain how to find explicit forms of these
integrable potentials for small $k$.

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