Real Algebraic and Analytic Geometry
Submission: 2004, December 17.
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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