Implicit function theorem for locally blow-analytic functions
[Théorème des fonctions implicites pour les fonctions localement "blow-analytiques"]
Annales de l'Institut Fourier, Tome 51 (2001) no. 4, pp. 1089-1100.

Nous montrons le théorème des fonctions implicites pour les fonctions localement "blow- analytiques" et, comme application de l'utilisation des homéomorphismes "blow- analytiques", nous donnons une méthode très facile pour résoudre les singularités des courbes analytiques.

In this paper we prove the implicit function theorem for locally blow-analytic functions, and as an interesting application of using blow-analytic homeomorphisms, we describe a very easy way to resolve singularities of analytic curves.

DOI : 10.5802/aif.1846
Classification : 58C05, 58K99, 14Pxx
Keywords: blow-analytic, arc-analytic
Mot clés : blow-analytique, arc-analytique
Paunescu, Laurentiu 1

1 University of Sydney, School of Mathematics and statistics, Sydney NSW 2006 (Australie)
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Paunescu, Laurentiu. Implicit function theorem for locally blow-analytic functions. Annales de l'Institut Fourier, Tome 51 (2001) no. 4, pp. 1089-1100. doi : 10.5802/aif.1846. http://archive.numdam.org/articles/10.5802/aif.1846/

[1] C. Camacho; P. Sad Invariant varieties through singularities of holomorphic vector fields, Annals of Math., Volume 115 (1982) | MR | Zbl

[1] E. Bierstone; P. D. Milman Arc-analytic functions, Invent. Math., Volume 101 (1990), pp. 411-424 | DOI | MR | Zbl

[2] T. Fukui; S. Koike; T.-C. Kuo Blow-analytic equisingularities, properties, problems and progress, Real analytic and algebraic singularities (Pitman Research Notes in Mathematics Series), Volume 381 (1997), pp. 8-29 | Zbl

[3] T. Fukui; T.-C. Kuo; L. Paunescu Constructing blow-analytic homeomorphisms (Submitted)

[4] H. Hironaka Introduction to real-analytic sets and real-analytic maps, Quaderni dei Gruppi di Ricerca Matematica del Consiglio Nazionale delle Ricerche (1973)

[5] M. Kobayashi; T.-C. Kuo On Blow-analytic equivalence of embedded curve singularities, Real analytic and algebraic singularities (Pitman Research Notes in Mathematics Series), Volume 381 (1997), pp. 30-37 | Zbl

[6] T.-C. Kuo The modified analytic trivialization of singularities, J. Math. Soc. Japan, Volume 32 (1980), pp. 605-614 | DOI | MR | Zbl

[7] T.-C. Kuo On classification of real singularities, Invent. Math., Volume 82 (1985), pp. 257-262 | DOI | MR | Zbl

[8] T.-C. Kuo; J. N. Ward A Theorem on almost analytic equisingularity, J. Math. Soc. Japan, Volume 33 (1981), pp. 471-484 | DOI | MR | Zbl

[9] K. Kurdyka Ensembles semi-algébriques symétriques par arcs, Math. Ann., Volume 282 (1988), pp. 445-462 | DOI | MR | Zbl

[10] K. Kurdyka Points réguliers d'un sous-analytique, Ann. Inst. Fourier, Grenoble, Volume 38 (1988) no. 1, pp. 133-156 | DOI | Numdam | MR | Zbl

[11] A. Parusiński Subanalytic Functions, Trans. of the A.M.S, Volume 344 (1994) no. 2, pp. 583-595 | DOI | MR | Zbl

[12] A. Parusiński Lipschitz stratification of subanalytic sets, Ann. École Norm. Sup., Volume tome 27 (1994) no. 6, pp. 661-696 | Numdam | MR | Zbl

[13] L. Paunescu An example of blow-analytic homeomorphism, Real analytic and algebraic singularities (Pitman Research Notes in Mathematics Series), Volume 381 (1997), pp. 62-63 | Zbl

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