Full paper in PDF:
$% D. D’Acunto and V. Grandjean, A gradient inequality at infinity for tame functions,
Rev. Mat. Complut. 18 (2005), no. 2, 493–501.%$
A Gradient Inequality at Infinity for Tame Functions
Dipartimento di Matematica Universitàá degli Studi di Pisa Via Filippo Buonarotti 2 56127 Pisa — Italia | Department of Computer Science University of Bath BATH BA2 7AY — England (UK) |
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.