Abstract
We start the part devoted to applications with three important non-academic models: the homogeneous potentials, the Bianchi IX cosmological model and the Sitnikov system in celestial mechanics. We note that, from the differential Galois theory of Chapter 2 (we shall need only the theorem of Kimura and the algorithm of Kovacic) and from our results of Chapter 4, the methods proposed here are completely systematic and elementary. In our opinion, this reflects the fact that the natural setting to obtain non-integrability results, using an analysis of the variational equations (along a particular integral curve), is the differential Galois theory.
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© 1999 Springer Basel AG
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Ruiz, J.J.M. (1999). Three Models. In: Differential Galois Theory and Non-Integrability of Hamiltonian Systems. Progress in Mathematics, vol 179. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8718-2_5
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DOI: https://doi.org/10.1007/978-3-0348-8718-2_5
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9741-9
Online ISBN: 978-3-0348-8718-2
eBook Packages: Springer Book Archive