The reduced Bautin index of planar vector fields



Duke Mathematical Journal

The reduced Bautin index of planar vector fields

H. Hauser, J.-J. Risler, and B. Teissier

Source: Duke Math. J. Volume 100, Number 3 (1999), 425-445.

First Page PDF: View first page of article (PDF, 36 KB)

Primary Subjects: 34C07
Secondary Subjects: 34A25, 34M99

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077227494
Mathematical Reviews number (MathSciNet): MR1719738
Zentralblatt MATH identifier: 0947.34013
Digital Object Identifier: doi:10.1215/S0012-7094-99-10015-9

References

[B] N. N. Bautin, On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or center type, American Math. Soc. Translation 1954 (1954), no. 100, 19.
Mathematical Reviews (MathSciNet): MR15,527h
Zentralblatt MATH: 0059.08201
[BY] M. Briskin and Y. Yomdin, Algebraic families of analytic functions. I, J. Differential Equations 136 (1997), no. 2, 248–267.
Mathematical Reviews (MathSciNet): MR98h:34009b
Zentralblatt MATH: 0886.34005
Digital Object Identifier: doi:10.1006/jfan.1996.3029
[Fe] Azzeddine Fekak, Interprétation algébrique de l'exposant de Łojasiewicz, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), no. 4, 193–196.
Mathematical Reviews (MathSciNet): MR91f:14053
Zentralblatt MATH: 0706.14036
[FY] J.-P. Francoise and Y. Yomdin, Bernstein inequalities and applications to analytic geometry and differential equations, J. Funct. Anal. 146 (1997), no. 1, 185–205.
Mathematical Reviews (MathSciNet): MR98h:34009c
Zentralblatt MATH: 0869.34008
Digital Object Identifier: doi:10.1006/jfan.1996.3029
[Ga] André Galligo, Théorème de division et stabilité en géométrie analytique locale, Ann. Inst. Fourier (Grenoble) 29 (1979), no. 2, vii, 107–184.
Mathematical Reviews (MathSciNet): MR81e:32009
Zentralblatt MATH: 0412.32011
[GM] M. Giusti and T. Mora, The complexity of Gröbner basis, preprint, 1994.
[HM] Herwig Hauser and Gerd Müller, A rank theorem for analytic maps between power series spaces, Inst. Hautes Études Sci. Publ. Math. (1994), no. 80, 95–115 (1995).
Mathematical Reviews (MathSciNet): MR96b:46065
[LT] M. Lejeune-Jalabert and B. Teissier, Clôture intégrale des idéaux et équisingularité, Sém. École Polytech., Publ. Institut Fourier, Grenoble, 1974.
[LiT] Joseph Lipman and Bernard Teissier, Pseudorational local rings and a theorem of Briançon-Skoda about integral closures of ideals, Michigan Math. J. 28 (1981), no. 1, 97–116.
Mathematical Reviews (MathSciNet): MR82f:14004
Zentralblatt MATH: 0464.13005
Digital Object Identifier: doi:10.1307/mmj/1029002461
Project Euclid: euclid.mmj/1029002461
[M] Maurice Mignotte, Mathématiques pour le calcul formel, Mathématiques. [Mathematics], Presses Universitaires de France, Paris, 1989.
Mathematical Reviews (MathSciNet): MR91a:68001
Zentralblatt MATH: 0679.12001
[MW] P. Monsky and G. Washnitzer, Formal cohomology. I, Ann. of Math. (2) 88 (1968), 181–217.
Mathematical Reviews (MathSciNet): MR40:1395
Zentralblatt MATH: 0162.52504
Digital Object Identifier: doi:10.2307/1970571
[NW] Y. Nesterenko and M. Waldschmidt, “On the approximation of the values of exponential function and logarithm by algebraic numbers“ (in Russian), Diophantine Approximations: Proceedings of Papers Dedicated to the Memory of Prof. N. I. Feldman, Mat. Zapiski, vol. 2, Centre for Applied Research Under Mech.-Math. Faculty of MSU, Moscow, 1996, pp. 23–42.
[So] Pablo Solernó, Effective Łojasiewicz inequalities in semialgebraic geometry, Appl. Algebra Engrg. Comm. Comput. 2 (1991), no. 1, 2–14.
Mathematical Reviews (MathSciNet): MR94i:14059
Zentralblatt MATH: 0754.14035
[Ya] S. Yakovenko, A geometric proof of the Bautin theorem, Concerning the Hilbert 16th problem, Amer. Math. Soc. Transl. Ser. 2, vol. 165, Amer. Math. Soc., Providence, RI, 1995, pp. 203–219.
Mathematical Reviews (MathSciNet): MR96j:34056
Zentralblatt MATH: 0828.34026

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