Real Algebraic and Analytic Geometry Preprint Server

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Submission: 2003, March 5.

Abstract:
Let $f: \mathbb{R}^n \rightarrow \mathbb{R}$ be a function of class $C^2$ definable in an o-minimal structure. We prove that the flow of the gradient field $\nabla f$ embeds each connected component of a non singular asymptotic critical level of $f$ into some connected component of a typical level of $f$. We apply this result to non singular complex polynomials.

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