A Gradient Inequality at Infinity for Tame Functions

  • Didier D’acunto
  • Vincent Grandjean
DOI: https://doi.org/10.5209/rev_REMA.2005.v18.n2.16699
Keywords: Lojasiewicz inequality, Asymptotic critical values, Bifurcation values, Gradient trajectories, O-minimal structures

Abstract

Let f be a C1 function defined over Rn and definable in a given o-minimal structure M expanding the real field. We prove here a gradient-like inequality at infinity in a neighborhood of an asymptotic critical value c. When f is C2 we use this inequality to discuss the trivialization by the gradient flow of f in a neighborhood of a regular asymptotic critical level.

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Published
2005-09-27
How to Cite
D’acunto D. y Grandjean V. (2005). A Gradient Inequality at Infinity for Tame Functions. Revista Matemática Complutense, 18(2), 493-501. https://doi.org/10.5209/rev_REMA.2005.v18.n2.16699
Issue
Vol. 18 No. 2 (2005)
Section
Articles

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