On the limit set at infinity of a gradient trajectory of a semialgebraic function

DOI10.1016/J.JDE.2006.10.009zbMath1128.32006OpenAlexW2009934967MaRDI QIDQ863919

Vincent Grandjean

Publication date: 12 February 2007

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2006.10.009

zbMATH Keywords

characteristic exponentgradient trajectorieslimit of secants

Mathematics Subject Classification ID

Semi-analytic sets, subanalytic sets, and generalizations (32B20)

Related Items (3)

Tangencies and polynomial optimization ⋮ A convex function satisfying the Łojasiewicz inequality but failing the gradient conjecture both at zero and infinity ⋮ Gradient trajectories for plane singular metrics. I: Oscillating trajectories

Cites Work

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• Bifurcation sets of functions definable in \(o\)-minimal structures
• Stratifications de Whitney et théorème de Bertini-Sard
• On the dynamics of gradients. Existence of invariant manifolds
• Sur la topologie des fibres d'une fonction définissable dans une structure o-minimale. (On the topology of fibers of functions definable in an o-minimal structure)
• Semialgebraic Sard theorem for generalized critical values.
• On gradient at infinity of semialgebraic functions
• Proof of the gradient conjecture of R. Thom.

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