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$% D. D’Acunto and V. Grandjean, A gradient inequality at infinity for tame functions, Rev. Mat. Complut. 18 (2005), no. 2, 493–501.%$
A Gradient Inequality at Infinity for Tame Functions
Let be a function defined over and definable in a given o-minimal structure expanding the real field. We prove here a gradient-like inequality at infinity in a neighborhood of an asymptotic critical value . When is we use this inequality to discuss the trivialization by the gradient flow of in a neighborhood of a regular asymptotic critical level.
Key words: Łojasiewicz inequality, asymptotic critical values, bifurcation values,
gradient trajectories, o-minimal structures.
2000 Mathematics Subject Classification: Primary 03C64, 34A26; Secondary 34C08.