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首页> 外文期刊>Discrete and Continuous Dynamical Systems, Series S >HYPERBOLICITY FOR SYMMETRIC PERIODIC ORBITS INTHE ISOSCELES THREE BODY PROBLEM
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HYPERBOLICITY FOR SYMMETRIC PERIODIC ORBITS INTHE ISOSCELES THREE BODY PROBLEM

机译：HYPERBOLICITY FOR SYMMETRIC PERIODIC ORBITS INTHE ISOSCELES THREE BODY PROBLEM

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摘要

We study the isosceles three body problem with fixed symmetryline for arbitrary masses, as a subsystem of the N-body problem. Our goal is toconstruct minimizing noncollision periodic orbits using a symmetric variationalmethod with a finite order symmetry group. The solution of this variationalproblem gives existence of noncollision periodic orbits which realize certainsymbolic sequences of rotations and oscillations in the isosceles three bodyproblem for any choice of the mass ratio. The Maslov index for these periodicorbits is used to prove the main result, Theorem 4.1, which states that the min-imizing curves in the three dimensional reduced energy momentum surface canbe extended to periodic curves which are generically hyperbolic. This remindsone of a theorem of Poincare 8, concerning minimizing periodic geodesics onorientable 2D surfaces. The results in this paper are novel in two directions:in addition to the higher dimensional setting, the minimization in the currentproblem is over a symmetry class, rather than a loop space.

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