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April  2005, 13(1): 139-162. doi: 10.3934/dcds.2005.13.139

Two-parameter families of implicit differential equations

Farid Tari 1,

1. 

ICMC-USP, Dept. de Matemática, Av. do Trabalhador São-Carlense, 400 Centro, Caixa Postal 668, CEP 13560-970, São Carlos (SP), Brazil

Received  January 2004 Revised  December 2004 Published  March 2005

We study in this paper local codimension 2 singularities of (first order) implicit differential equations $F(x,y,p)=0$, where $F$ is a germ of a smooth function, $p=\frac{dy}{dx}$, $F_p=0$ and $F_{p p}\ne 0$ at the singular point. We obtain topological models of these singularities and deal with their bifurcations in generic 2-parameter families of equations.
Keywords: singularities, Implicit differential equations, bifurcations..
Mathematics Subject Classification: 34A09, 37G10, 37C10, 58K05, 53A0.
Citation: Farid Tari. Two-parameter families of implicit differential equations. Discrete and Continuous Dynamical Systems, 2005, 13 (1) : 139-162. doi: 10.3934/dcds.2005.13.139
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