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July  2000, 6(3): 519-536. doi: 10.3934/dcds.2000.6.519

On pairs of differential $1$-forms in the plane

R.D.S. Oliveira 1, and  F. Tari 1,

1. 

Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, Caixa Postal 668, CEP 13560-970, São Carlos (SP), Brazil, Brazil

Received  May 1999 Revised  March 2000 Published  April 2000

We classify pairs of germs of differential $1$-forms $(\alpha, beta)$ in the plane, where $\alpha$, $beta$ are either regular or have a singularity of type saddle/node/focus. The main tools used here are singularity theory and the method of polar blowing up. We also present a desingularization theorem for pairs of germs of differential $1$-forms in the plane.
Keywords: desingularization., Differential 1-forms, pairs of foliations.
Mathematics Subject Classification: 34C20, 34A34, 58C2.
Citation: R.D.S. Oliveira, F. Tari. On pairs of differential $1$-forms in the plane. Discrete & Continuous Dynamical Systems - A, 2000, 6 (3) : 519-536. doi: 10.3934/dcds.2000.6.519
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