Celestial Mechanics and Dynamical Astronomy

, Volume 115, Issue 4, pp 397–404

A note on algebraic potentials and Morales–Ramis theory

Original Article

DOI: 10.1007/s10569-013-9470-2

Cite this article as:
Combot, T. Celest Mech Dyn Astr (2013) 115: 397. doi:10.1007/s10569-013-9470-2


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.


Non-integrability Homogeneous potentials Differential Galois theory 

Mathematics Subject Classfication (2000)

MSC 37J30 MSC 70F15 

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.IMCCEParisFrance

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