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Displaying similar documents to “Instability of equilibria in dimension three”

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...

On real algebraic links in S 3

R. Benedetti, M. Shiota (1998)

Bollettino dell'Unione Matematica Italiana

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Viene presentata una costruzione che, dato un arbitrario nodo L ⊆ S 3 , produce allo stesso tempo: 1) un'applicazione polinomiale f : R 4 , 0 → R 2 , 0 con singolarità (debolmente) isolata in 0 e L come tipo di nodo della singolarità; 2) una risoluzione delle singolarità di f nel senso di Hironaka. Specializzando la costruzione ai nodi fibrati otteniamo una versione debole (a meno di scoppiementi e nella categoria analitica reale) di un reciproco per il teorema di fibrazione di Milnor.

On the existence of canard solutions

Daniel Panazzolo (2000)

Publicacions Matemàtiques

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We study the existence of global canard surfaces for a wide class of real singular perturbation problems. These surfaces define families of solutions which remain near the slow curve as the singular parameter goes to zero.