Geodesic
Completion of the classification of generic singularities of geodesic
Izvestiya. Mathematics , Tome 83 (2019) no. 1, pp. 104-123

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This is the final paper in a series devoted to generic singularities of geodesic flows for two-dimensional pseudo-Riemannian metrics of changing signature and metrics induced from the Euclidean metric of the ambient space on surfaces with a cuspidal edge. We study the local phase portraits and the properties of geodesics at degenerate points of a certain type. This completes the list of singularities in codimensions $1$ and $2$.
Keywords: pseudo-Riemannian metric, geodesic, singular point, normal form, invariant manifold. 
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     author = {N. G. Pavlova and A. O. Remizov},
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N. G. Pavlova; A. O. Remizov. Completion of the classification of generic singularities of geodesic. Izvestiya. Mathematics , Tome 83 (2019) no. 1, pp. 104-123. http://geodesic.mathdoc.fr/item/IM2_2019_83_1_a4/