A gradient inequality at infinity for tame functions.

D'Acunto, Didier, and Grandjean, Vincent. "A gradient inequality at infinity for tame functions.." Revista Matemática Complutense 18.2 (2005): 493-501. <http://eudml.org/doc/38179>.

@article{DAcunto2005,
abstract = {Let f be a C1 function defined over Rn and definable in a given o-minimal structure M expanding the real field. We prove here a gradient-like inequality at infinity in a neighborhood of an asymptotic critical value c. When f is C2 we use this inequality to discuss the trivialization by the gradient flow of f in a neighborhood of a regular asymptotic critical level.},
author = {D'Acunto, Didier, Grandjean, Vincent},
journal = {Revista Matemática Complutense},
keywords = {Ecuaciones diferenciales ordinarias; Geometría algebraica; Desigualdades; Gradientes; Desigualdad de Lojasiewicz; Łojasiewicz inequality; asymptotic critical values; bifurcation values; gradient trajectories; o-minimal structures},
language = {eng},
number = {2},
pages = {493-501},
title = {A gradient inequality at infinity for tame functions.},
url = {http://eudml.org/doc/38179},
volume = {18},
year = {2005},
}

TY - JOUR
AU - D'Acunto, Didier
AU - Grandjean, Vincent
TI - A gradient inequality at infinity for tame functions.
JO - Revista Matemática Complutense
PY - 2005
VL - 18
IS - 2
SP - 493
EP - 501
AB - Let f be a C1 function defined over Rn and definable in a given o-minimal structure M expanding the real field. We prove here a gradient-like inequality at infinity in a neighborhood of an asymptotic critical value c. When f is C2 we use this inequality to discuss the trivialization by the gradient flow of f in a neighborhood of a regular asymptotic critical level.
LA - eng
KW - Ecuaciones diferenciales ordinarias; Geometría algebraica; Desigualdades; Gradientes; Desigualdad de Lojasiewicz; Łojasiewicz inequality; asymptotic critical values; bifurcation values; gradient trajectories; o-minimal structures
UR - http://eudml.org/doc/38179
ER -