A note on algebraic potentials and Morales–Ramis theory
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- Combot, T. Celest Mech Dyn Astr (2013) 115: 397. doi:10.1007/s10569-013-9470-2
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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 potential, and thus making this analysis unavoidable.