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Periodic Solutions

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Part of the Grundlehren der mathematischen Wissenschaften book series (volume 187)

Abstract

The theorem of Sundman discussed in chapter one represents the most far reaching result yet known about general solutions to the three- body problem. Unfortunately his ingenious method cannot be extended to the case n > 3. Although the results in § 6 can be used to exclude at the outset the simultaneous collision of all n bodies, the investigations of § 12, § 13 show that already a triple collision may give rise to essential singularities.

Keywords

  • Periodic Solution
  • Normal Form
  • Power Series
  • Hamiltonian System
  • Equilibrium Solution

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© 1995 Springer-Verlag Berlin Heidelberg

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Siegel, C.L., Moser, J.K. (1995). Periodic Solutions. In: Lectures on Celestial Mechanics. Grundlehren der mathematischen Wissenschaften, vol 187. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-87284-6_2

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  • DOI: https://doi.org/10.1007/978-3-642-87284-6_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58656-2

  • Online ISBN: 978-3-642-87284-6

  • eBook Packages: Springer Book Archive