Implicit function theorem for locally blow-analytic functions

Laurentiu Paunescu[1]

  • [1] University of Sydney, School of Mathematics and statistics, Sydney NSW 2006 (Australie)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 4, page 1089-1100
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Paunescu, Laurentiu. "Implicit function theorem for locally blow-analytic functions." Annales de l’institut Fourier 51.4 (2001): 1089-1100. <http://eudml.org/doc/115935>.

@article{Paunescu2001,
abstract = {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.},
affiliation = {University of Sydney, School of Mathematics and statistics, Sydney NSW 2006 (Australie)},
author = {Paunescu, Laurentiu},
journal = {Annales de l’institut Fourier},
keywords = {blow-analytic; arc-analytic; implicit function theorem; blow-analytic category; local blow-analytic functions},
language = {eng},
number = {4},
pages = {1089-1100},
publisher = {Association des Annales de l'Institut Fourier},
title = {Implicit function theorem for locally blow-analytic functions},
url = {http://eudml.org/doc/115935},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Paunescu, Laurentiu
TI - Implicit function theorem for locally blow-analytic functions
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 4
SP - 1089
EP - 1100
AB - 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.
LA - eng
KW - blow-analytic; arc-analytic; implicit function theorem; blow-analytic category; local blow-analytic functions
UR - http://eudml.org/doc/115935
ER -

References

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  1. C. Camacho, P. Sad, Invariant varieties through singularities of holomorphic vector fields, Annals of Math. 115 (1982) Zbl0503.32007MR657239
  2. E. Bierstone, P. D. Milman, Arc-analytic functions, Invent. Math. 101 (1990), 411-424 Zbl0723.32005MR1062969
  3. T. Fukui, S. Koike, T.-C. Kuo, Blow-analytic equisingularities, properties, problems and progress, Real analytic and algebraic singularities 381 (1997), 8-29, Longman Zbl0954.26012
  4. T. Fukui, T.-C. Kuo, L. Paunescu, Constructing blow-analytic homeomorphisms Zbl0984.32005
  5. H. Hironaka, Introduction to real-analytic sets and real-analytic maps, Quaderni dei Gruppi di Ricerca Matematica del Consiglio Nazionale delle Ricerche (1973), Istituto Matematico "L. Tonelli" dell'Università di Pisa 
  6. M. Kobayashi, T.-C. Kuo, On Blow-analytic equivalence of embedded curve singularities, Real analytic and algebraic singularities 381 (1997), 30-37, Longman Zbl0899.32002
  7. T.-C. Kuo, The modified analytic trivialization of singularities, J. Math. Soc. Japan 32 (1980), 605-614 Zbl0509.58007MR589100
  8. T.-C. Kuo, On classification of real singularities, Invent. Math. 82 (1985), 257-262 Zbl0587.32018MR809714
  9. T.-C. Kuo, J. N. Ward, A Theorem on almost analytic equisingularity, J. Math. Soc. Japan 33 (1981), 471-484 Zbl0476.58004MR620284
  10. K. Kurdyka, Ensembles semi-algébriques symétriques par arcs, Math. Ann. 282 (1988), 445-462 Zbl0686.14027MR967023
  11. K. Kurdyka, Points réguliers d'un sous-analytique, Ann. Inst. Fourier, Grenoble 38 (1988), 133-156 Zbl0619.32007MR949002
  12. A. Parusi#x0144;ski, Subanalytic Functions, Trans. of the A.M.S 344 (1994), 583-595 Zbl0819.32006
  13. A. Parusi#x0144;ski, Lipschitz stratification of subanalytic sets, Ann. École Norm. Sup. tome 27 (1994), 661-696 Zbl0819.32007MR1307677
  14. L. Paunescu, An example of blow-analytic homeomorphism, Real analytic and algebraic singularities 381 (1997), 62-63, Longman Zbl0896.58012

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