Exposants de Łojasiewicz pour les fonctions semi-algébriques

Azzeddine Fekak

Annales Polonici Mathematici (1992)

  • Volume: 56, Issue: 2, page 123-131
  • ISSN: 0066-2216

Abstract

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We prove the rationality of the Łojasiewicz exponent for semialgebraic functions without compactness hypothesis. In the parametric situation, we show that the parameter space can be divided into a finite number of semialgebraic sets on each of which the Łojasiewicz exponent is constant.

How to cite

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Azzeddine Fekak. "Exposants de Łojasiewicz pour les fonctions semi-algébriques." Annales Polonici Mathematici 56.2 (1992): 123-131. <http://eudml.org/doc/262403>.

@article{AzzeddineFekak1992,
author = {Azzeddine Fekak},
journal = {Annales Polonici Mathematici},
keywords = {semialgebraic; Łojasiewicz inequality; real spectrum; Nullstellensatz; semialgebraic functions; semialgebraic subset; real closed field; Łojasiewicz set; Łojasiewicz exponent},
language = {fre},
number = {2},
pages = {123-131},
title = {Exposants de Łojasiewicz pour les fonctions semi-algébriques},
url = {http://eudml.org/doc/262403},
volume = {56},
year = {1992},
}

TY - JOUR
AU - Azzeddine Fekak
TI - Exposants de Łojasiewicz pour les fonctions semi-algébriques
JO - Annales Polonici Mathematici
PY - 1992
VL - 56
IS - 2
SP - 123
EP - 131
LA - fre
KW - semialgebraic; Łojasiewicz inequality; real spectrum; Nullstellensatz; semialgebraic functions; semialgebraic subset; real closed field; Łojasiewicz set; Łojasiewicz exponent
UR - http://eudml.org/doc/262403
ER -

References

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  1. [1] J. Bochnak, M. Coste et M. F. Roy, Géométrie algébrique réelle, Ergeb. Math. Grenzgeb. (3) 12, Springer, 1987. Zbl0633.14016
  2. [2] J. Bochnak et J. J. Risler, Sur les exposants de Łojasiewicz, Comment. Math. Helv. 50 (1975), 493-507. 
  3. [3] T.-C. Kuo, Computation of Łojasiewicz exponent of f(x,y), ibid. 49 (1974), 201-213. Zbl0291.58004
  4. [4] M. Lejeune et B. Teissier, Dépendance intégrale sur les idéaux et équisingularité, Séminaire Ecole Polytechnique, Publ. Inst. Fourier, 1974. 
  5. [5] B. Lichtin, Estimation of Łojasiewicz exponents and Newton polygons, Invent. Math. 64 (1981), 417-429. Zbl0556.32003
  6. [6] S. Łojasiewicz, Ensembles semi-analytiques, notes multigraphiées, I.H.E.S., 1965. 
  7. [7] G. Raby, Théorème des zéros sous-analytiques et inégalités de Łojasiewicz, dans : Lecture Notes in Math. 1028, Springer, 1983, 253-265. 
  8. [8] R. Walker, Algebraic Curves, Dover, 1962. Zbl0103.38202

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