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Laurentiu Paunescu
Implicit function theorem for locally blow-analytic functions
(Théorème des fonctions implicites pour les fonctions localement "blow-analytiques")
Annales de l'institut Fourier, 51 no. 4 (2001), p. 1089-1100, doi: 10.5802/aif.1846
Article PDF | Reviews Zbl 0996.58008
Class. Math.: 58C05, 58K99, 14Pxx
Keywords: blow-analytic, arc-analytic

Résumé - Abstract

In this paper we prove the implicit function theorem for {\sl 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.

Bibliography

[1] C. Camacho & P. Sad, “Invariant varieties through singularities of holomorphic vector fields”, Annals of Math. 115 (1982)  MR 657239 |  Zbl 0503.32007
[1] E. Bierstone & P. D. Milman, “Arc-analytic functions”, Invent. Math. 101 (1990), p. 411-424 Article |  MR 1062969 |  Zbl 0723.32005
[2] T. Fukui, S. Koike & T.-C. Kuo, Blow-analytic equisingularities, properties, problems and progress, Pitman Research Notes in Mathematics Series, Longman, 1997, p. 8-29  Zbl 0954.26012
[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, 1973
[5] M. Kobayashi & T.-C. Kuo, On Blow-analytic equivalence of embedded curve singularities, Pitman Research Notes in Mathematics Series, Longman, 1997, p. 30-37  Zbl 0899.32002
[6] T.-C. Kuo, “The modified analytic trivialization of singularities”, J. Math. Soc. Japan 32 (1980), p. 605-614 Article |  MR 589100 |  Zbl 0509.58007
[7] T.-C. Kuo, “On classification of real singularities”, Invent. Math. 82 (1985), p. 257-262 Article |  MR 809714 |  Zbl 0587.32018
[8] T.-C. Kuo & J. N. Ward, “A Theorem on almost analytic equisingularity”, J. Math. Soc. Japan 33 (1981), p. 471-484 Article |  MR 620284 |  Zbl 0476.58004
[9] K. Kurdyka, “Ensembles semi-algébriques symétriques par arcs”, Math. Ann. 282 (1988), p. 445-462 Article |  MR 967023 |  Zbl 0686.14027
[10] K. Kurdyka, “Points réguliers d'un sous-analytique”, Ann. Inst. Fourier, Grenoble 38 (1988) no. 1, p. 133-156 Cedram |  MR 949002 |  Zbl 0619.32007
[11] A. Parusi#x0144;ski, “Subanalytic Functions”, Trans. of the A.M.S 344 (1994) no. 2, p. 583-595 Article |  Zbl 0819.32006
[12] A. Parusi#x0144;ski, “Lipschitz stratification of subanalytic sets”, Ann. École Norm. Sup. tome 27 (1994) no. 6, p. 661-696 Numdam |  MR 1307677 |  Zbl 0819.32007
[13] L. Paunescu, An example of blow-analytic homeomorphism, Pitman Research Notes in Mathematics Series, Longman, 1997, p. 62-63  Zbl 0896.58012
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