Displaying similar documents to “On the existence of canard solutions”

Catastrophes and partial differential equations

John Guckenheimer (1973)

Annales de l'institut Fourier

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This paper outlines the manner in which Thom’s theory of catastrophes fits into the Hamilton-Jacobi theory of partial differential equations. The representation of solutions of a first order partial differential equation as lagrangian manifolds allows one to study the local structure of their singularities. The structure of generic singularities is closely related to Thom’s concept of the elementary catastrophe associated to a singularity. Three concepts of the stability of a singularity...

Non oscillating solutions of analytic gradient vector fields

Fernando Sanz (1998)

Annales de l'institut Fourier

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Let γ be an integral solution of an analytic real vector field ξ defined in a neighbordhood of 0 ∈ ℝ 3 . Suppose that γ has a single limit point, ω ( γ ) = { 0 } . We say that γ is non oscillating if, for any analytic surface H , either γ is contained in H or γ cuts H only finitely many times. In this paper we give a sufficient condition for γ to be non oscillating. It is established in terms of the existence of “generalized iterated tangents”, i.e. the existence of a single limit point for any transform property...

Instability of equilibria in dimension three

Marco Brunella (1998)

Annales de l'institut Fourier

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In this paper we show that if v is an analytic vector field on ℝ 3 having an isolated singular point at 0, then there exists a trajectory of v which converges to 0 in the past or in the future. The proof is based on certain results concerning desingularizaton of vector fields in dimension three and on index-type arguments .