On the entire and finite valued solutions of the three-body problem. (English) Zbl 1482.70008
Summary: A full list of entire and finite valued solutions of the three body problem in the form of functions, depending on a time variable, is established. All the entire and finite valued solutions are among the solutions of Euler and Lagrange.
MSC:
| 70F07 | Three-body problems |
| 34M30 | Asymptotics and summation methods for ordinary differential equations in the complex domain |
| 74H10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics |
| 34M45 | Ordinary differential equations on complex manifolds |
| 74H05 | Explicit solutions of dynamical problems in solid mechanics |
Keywords:
three-body problem; factorization of the flow; first integral; singular points; analytic functions; entire functions; compact holomorphic manifold; holomorphic foliationReferences:
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