Geometric properties of the integral curves of an implicit differential equation

Farid Tari

doi:10.3934/dcds.2007.17.349

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2007, Volume 17, Issue 2: 349-364. Doi: 10.3934/dcds.2007.17.349

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Geometric properties of the integral curves of an implicit differential equation

Farid Tari^1,

1.
Department of Mathematical Sciences, University of Durham, Science Laboratories, South Road, Durham DH1 3LE

Received: December 2005

Revised: September 2006

Published: May 2007

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Abstract

We study geometric properties of the integral curves of an implicit differential equation in a neighbourhood of a codimension $\le 1$ singularity. We also deal with the way these singularities bifurcate in generic families of equations and the changes in the associated geometry. The main tool used here is the Legendre transformation.

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Mathematics Subject Classification: 34A09, 37G10, 37C10, 53A05, 58K05.

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