Generic singularities of implicit systems of first order differential equations on the plane

2003/02/12 by A. A. Davydov, Davydov, A. A., G. Ishikawa +5
Mathematics · #37G05 #37Jxx #58K45 #58K50 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #math.DG #math.DS #msc:37G05 #msc:37Jxx #msc:58K45 #msc:58K50

paper · pdf · doi:10.48550/arxiv.math/0302134

28 pages, 4 figures

arxiv created 2003/02/12 · arxiv updated 2009/11/30

Abstract

For the implicit systems of first order ordinary differential equations on the plane there is presented the complete local classification of generic singularities of family of its phase curves up to smooth orbital equivalence. Besides the well known singularities of generic vector fields on the plane and the singularities described by a generic first order implicit differential equations, there exists only one generic singularity described by the implicit first order equation supplied by Whitney umbrella surface generically embedded to the space of directions on the plane.

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