A note on algebraic potentials and Morales-Ramis theory

Abstract

We present various properties of algebraic potentials, and then prove that some Morales-Ramis theorems readily apply for such potentials even if they are not in general meromorphic potentials. This allows in particular to precise some non-integrability proofs in celestial mechanics, where the mutual distances between the bodies appear in the potentials, and thus making this analysis unavoidable.

8 pages

References in corpus (2)

• On some exceptional cases in the integrability of the three-body problem
• Non integrability of the n body problem with non zero angular momentum

Cited by in corpus (9)

• Note on integrability of certain homogeneous Hamiltonian systems
• Non-integrability of the dumbbell and point mass problem
• Destructive relativity
• Integrable homogeneous potentials of degree $-1$ in the plane with small eigenvalues
• Non integrability of a self-gravitating Riemann liquid ellipsoid
• Non-integrability of the Kepler and the two-body problem on the Heisenberg group
• Meromorphically integrable homogeneous potentials with multiple Darboux points
• Translational dynamics of diatomic molecule in magnetic quadrupole trap
• Non-integrability of charged three-body problem