A constructive proof of the Density of Algebraic Pfaff Equations without Algebraic Solutions

S. C. Coutinho[1]

  • [1] Universidade Federal do Rio de Janeiro Departamento de Ciência da Computação Instituto de Matemática P.O. Box 68530, 21945-970 Rio de Janeiro, RJ (Brazil) Programa de Engenharia de Sistemas e Computação COPPE, UFRJ, PO Box 68511 21941-972, Rio de Janeiro, RJ (Brazil)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 5, page 1611-1621
  • ISSN: 0373-0956

Abstract

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We present a constructive proof of the fact that the set of algebraic Pfaff equations without algebraic solutions over the complex projective plane is dense in the set of all algebraic Pfaff equations of a given degree.

How to cite

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Coutinho, S. C.. "A constructive proof of the Density of Algebraic Pfaff Equations without Algebraic Solutions." Annales de l’institut Fourier 57.5 (2007): 1611-1621. <http://eudml.org/doc/10272>.

@article{Coutinho2007,
abstract = {We present a constructive proof of the fact that the set of algebraic Pfaff equations without algebraic solutions over the complex projective plane is dense in the set of all algebraic Pfaff equations of a given degree.},
affiliation = {Universidade Federal do Rio de Janeiro Departamento de Ciência da Computação Instituto de Matemática P.O. Box 68530, 21945-970 Rio de Janeiro, RJ (Brazil) Programa de Engenharia de Sistemas e Computação COPPE, UFRJ, PO Box 68511 21941-972, Rio de Janeiro, RJ (Brazil)},
author = {Coutinho, S. C.},
journal = {Annales de l’institut Fourier},
keywords = {Pfaff equation; singularity; algebraic solution},
language = {eng},
number = {5},
pages = {1611-1621},
publisher = {Association des Annales de l’institut Fourier},
title = {A constructive proof of the Density of Algebraic Pfaff Equations without Algebraic Solutions},
url = {http://eudml.org/doc/10272},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Coutinho, S. C.
TI - A constructive proof of the Density of Algebraic Pfaff Equations without Algebraic Solutions
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 5
SP - 1611
EP - 1621
AB - We present a constructive proof of the fact that the set of algebraic Pfaff equations without algebraic solutions over the complex projective plane is dense in the set of all algebraic Pfaff equations of a given degree.
LA - eng
KW - Pfaff equation; singularity; algebraic solution
UR - http://eudml.org/doc/10272
ER -

References

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  8. J. P. Jouanolou, Equations de Pfaff algébriques, 708 (1979), Springer-Verlag, Heidelberg Zbl0477.58002MR537038
  9. S. Lang, Algebra, (1974), Addison-Wesley, Reading Zbl0848.13001MR197234
  10. A. J. Maciejewski, J. M. Ollagnier, A. Nowicki, J. -M. Strelcyn, Around Jouanolou non-integrability theorem, Indag. Mathem. 11 (2000), 239-254 Zbl0987.34005MR1813164
  11. A. L. Neto, Algebraic solutions of polynomial differential equations and foliations in dimension two, Holomorphic Dynamics 1345 (1988), 192-232, New York-Heidelberg-Berlin Zbl0677.58036MR980960
  12. J. M. Ollagnier, A. Nowicki, J. -M. Strelcyn, On the non-existence of constants of derivations: the proof of a theorem of Jouanolou and its development, Bull. Sci. math. 123 (1995), 195-233 Zbl0855.34010MR1327804
  13. M. J. Prelle, M. F. Singer, Elementary first integrals of differential equations, Trans. Amer. Math. Soc. 279 (1983), 215-229 Zbl0527.12016MR704611

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