# A gradient inequality at infinity for tame functions.

Didier D'Acunto; Vincent Grandjean

Revista Matemática Complutense (2005)

- Volume: 18, Issue: 2, page 493-501
- ISSN: 1139-1138

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topD'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 -

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