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arXiv · 1209.4747

A note on algebraic potentials and Morales-Ramis theory

Thierry Combot
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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.

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Thierry Combot. 2012-09-21. A note on algebraic potentials and Morales-Ramis theory. https://doi.org/10.1007/s10569-013-9470-2

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