Geodesic
Recurrent Geodesics in Flat Lorentz 3-Manifolds
Canadian mathematical bulletin, Tome 47 (2004) no. 3, pp. 332-342

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DOI

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 ${{\gamma }_{1}}$ , ${{\gamma }_{2}}$ , a unique geodesic forward spirals towards ${{\gamma }_{1}}$ and backward spirals towards ${{\gamma }_{2}}$ .
DOI : 10.4153/CMB-2004-032-5
Mots-clés : 57M50, 37B20, geometric structures on low-dimensional manifolds, notions of recurrence 
Charette, Virginie; Goldman, William M.; Jones, Catherine A. Recurrent Geodesics in Flat Lorentz 3-Manifolds. Canadian mathematical bulletin, Tome 47 (2004) no. 3, pp. 332-342. doi: 10.4153/CMB-2004-032-5
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     title = {Recurrent {Geodesics} in {Flat} {Lorentz} {3-Manifolds}},
     journal = {Canadian mathematical bulletin},
     pages = {332--342},
     year = {2004},
     volume = {47},
     number = {3},
     doi = {10.4153/CMB-2004-032-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-032-5/}
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