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.
KeywordsPeriodic Solution Normal Form Power Series Hamiltonian System Equilibrium Solution
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