A Hamiltonian system covering anisotropic Kepler and symmetric n-body reductions admits infinitely many periodic orbits on every compact energy surface when the anisotropy parameter sum condition holds.
Cristofaro-Gardiner, U
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Relative Periodic Orbits in the Gutzwiller-type Anisotropic Kepler Problem and $n$-body Problem
A Hamiltonian system covering anisotropic Kepler and symmetric n-body reductions admits infinitely many periodic orbits on every compact energy surface when the anisotropy parameter sum condition holds.