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

DOI10.1070/IM8723zbMath1458.53050OpenAlexW2889481028MaRDI QIDQ3120456

N. G. Pavlova, Alexey O. Remizov

Publication date: 4 March 2019

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/im8723

zbMATH Keywords

normal formsingular pointgeodesicinvariant manifoldpseudo-Riemannian metric

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Geodesics in global differential geometry (53C22) Geodesic flows in symplectic geometry and contact geometry (53D25) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (4)

Local analytic classification for quasi-linear implicit differential systems at transversal singular points ⋮ Singularities of quasi-linear differential equations ⋮ Hyperbolic Roussarie fields with degenerate quadratic part ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a class of vector fields with discontinuities of divide-by-zero type and its applications to geodesics in singular metrics
• On the local and global properties of geodesics in pseudo-Riemannian metrics
• Singularities of a geodesic flow on surfaces with a cuspidal edge
• Differential invariants of second order ODEs. I
• Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian
• A brief survey on singularities of geodesic flows in smooth signature changing metrics on 2-surfaces
• Nilpotent singularities in generic 4-parameter families of 3-dimensional vector fields
• Multidimensional Poincaré construction and singularities of lifted fields for implicit differential equations
• Singularities of the geodesic flow on surfaces with pseudo-Riemannian metrics
• Sur les singularités des formes différentielles
• Partially hyperbolic fixed points
• Point Classification of Second Order ODEs: Tresse Classification Revisited and Beyond
• Sign and geometric meaning of curvature
• A complete classification of generic singularities of geodesic flows on 2-surfaces with pseudo-Riemannian metrics
• On binary differential equations
• On binary differential equations and umbilics
• Geodesics on 2-surfaces with pseudo-Riemannian metric: singularities of changes of signature
• Invariant manifolds
• Impasse singularities of differential systems of the form \(A(x) x^{\prime} =F(x)\)

This page was built for publication: Completion of the classification of generic singularities of geodesic flows in two classes of metrics