Geometric properties of the integral curves of an implicit differential equation

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April 2007, 17(2): 349-364. doi: 10.3934/dcds.2007.17.349

Geometric properties of the integral curves of an implicit differential equation

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

Received December 2005 Revised September 2006 Published November 2006

Abstract
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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.

Keywords: Legendre transformation, Implicit differential equations, bifurcations., inflections.

Mathematics Subject Classification: 34A09, 37G10, 37C10, 53A05, 58K0.

Citation: Farid Tari. Geometric properties of the integral curves of an implicit differential equation. Discrete & Continuous Dynamical Systems - A, 2007, 17 (2) : 349-364. doi: 10.3934/dcds.2007.17.349

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