Non-oscillating solutions of analytic gradient vector fields

DOI10.5802/AIF.1648zbMath0909.34027OpenAlexW2319881224WikidataQ125887539 ScholiaQ125887539MaRDI QIDQ1271452

Fernando Sanz Sánchez

Publication date: 9 November 1998

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1998__48_4_1045_0

zbMATH Keywords

oscillationvector fieldgradientcenter manifolddesingularizationblowing-uptangent

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Modifications; resolution of singularities (complex-analytic aspects) (32S45) Invariant manifolds for ordinary differential equations (34C45)

Related Items (6)

Gradient Flows, Second-Order Gradient Systems and Convexity ⋮ A convex function satisfying the Łojasiewicz inequality but failing the gradient conjecture both at zero and infinity ⋮ On restricted analytic gradients on analytic isolated surface singularities ⋮ Gradient trajectories for plane singular metrics. I: Oscillating trajectories ⋮ On trajectories of analytic gradient vector fields ⋮ Gradient flow of a harmonic function in \(\mathbb{R}^3\)

Cites Work

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• Applications of centre manifold theory
• Thom's conjecture on singularities of gradient vector fields
• Finiteness theorems for Pfaffian manifolds
• Topological equivalence of normally hyperbolic dynamical systems
• On the dynamics of gradients. Existence of invariant manifolds
• Stability of the center-stable manifold
• Trajectoires non-oscillantes des champs de vecteurs gradients
• Invariant manifolds
• Proof of the gradient conjecture of R. Thom.

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