Completion of the classification of generic singularities of geodesic flows in two classes of metrics

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. © 2019 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.

Authors
Pavlova N.G. 1 , Remizov A.O.2, 3
Publisher
Institute of Physics Publishing
Number of issue
1
Language
English
Pages
104-123
Status
Published
Volume
83
Year
2019
Organizations
  • 1 Peoples' Friendship University of Russia, Moscow Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow Region, Russian Federation
  • 2 Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow Region, Russian Federation
  • 3 CMAP École Polytechnique, Palaiseau, France
Keywords
geodesic; invariant manifold; normal form; pseudo-Riemannian metric; singular point
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