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Exponential growth of the number of periodic orbits for three-body type problems. (English) Zbl 0801.70006

Summary: We study the number of periodic orbits for three-body type problems and their behavior. Assuming that the periodic orbits are non degenerate, we have an exponential growth of the number of period orbits. This result is a statement about the fixed period problem, we would like to have the same result for the fixed energy problem. The exponential growth for the fixed period problem does not imply the exponential growth for the fixed energy problem.

MSC:

70F07 Three-body problems
37G99 Local and nonlocal bifurcation theory for dynamical systems
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