Real Algebraic and Analytic Geometry |

A Gradient Inequality at infinity for tame functions.

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Submission: 2004, December 17.

*Abstract:
Given a definable function F enough differentiable defined
over R^n, we find a Lojasiewicz type inequality at infinity
satisfied by the gradient of the function F in a neighbourhood
of an asymptotic critical value c.
We use this result to discuss sufficient conditions to trivialise
by the gradient flow of F over a neighbourhood of c.*

Mathematics Subject Classification (2000): 03C64 34A26 34C08.

Keywords and Phrases: Lojasiewicz, o-minimality, gradient, asymptotic critical values.

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