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Generic singularities of implicit systems of first order differential equations on the plane. (English) Zbl 1183.37089

Author’s 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 the 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.
Reviewer: Timo Reis (Berlin)

MSC:

37G05 Normal forms for dynamical systems
34A09 Implicit ordinary differential equations, differential-algebraic equations
34A26 Geometric methods in ordinary differential equations
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