Virginie Charette, William M. Goldman, Catherine A. Jones
Let M be a complete flat Lorentz 3-manifold M with purely hyperbolic holonomy Gamma. Recurrent geodesic rays are completely classified when Gamma is cyclic. This implies that for any pair of periodic geodesics gamma1, gamma2, a unique geodesic forward spirals towards gamma1 and backward spirals towards gamma2.
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