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Cyclicite finie des polycycles hyperboliques de champs de vecteurs du plan mise sous forme normale

Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1455)

Keywords

Montre Alors Cette Equation Nous Aurons Aura Besoin 
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References

  1. [1]
    A. Mourtada:“ Cyclicité finie des polycycles hyperboliques de champs de vecteurs du Plan.-Algorithme de Finitude” (Preprint-Dijon).Google Scholar
  2. [2]
    A.A. Andronov, E.A. Leontovich, I.I. Gordon and A.G. Maier: “Theory of bifurcation of Dynamical Systems on the Plane”. Israel Program of Scientific Translations, Jerusalem, 1971.Google Scholar
  3. [3]
    L.A. Cherkas: “Structure of a successor function in the neighborhod of separatrix of a perturbed analytic autonomous system in the Plane”. Translated from differentsial’nye Uraneniya, vol. 17, no 3, March. 1981, pp. 469–478.Google Scholar
  4. [4]
    R. Roussarie: “A note on Finite Cyclicity Property and Hilbert’s 16 th Problem”. Dynamical Systems (Proc. Chilean Symp., Valparaiso 1986) (Lecture Notes in Mathematics 1331) ed R. Barmon, R. Labarca and J. Palis Jr (Berlin: Springer), pp 161–168.Google Scholar
  5. [5]
    H. Dulac: “Sur les cycles limites”. Bull. soc. Math. France, 51, (1923), pp 45–188.MathSciNetzbMATHGoogle Scholar
  6. [6]
    A. Mourtada: “Polycycles Hyperboliques Génériques à trois et quatre sommets”, (Preprint-Dijon).Google Scholar
  7. [7]
    S. Sternberg: “On the behaviour of invariant curves near a hyperbolic point of a surface transformation”. American Journal of Mathematics, vol. 75 (1955), pp. 526–534.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    S. Sternberg: “Local contractions and a theorem of Poincare”. American Journal of Mathematics, vol. 79 (1957), pp. 809–824.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    R. Roussarie: “On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields”. BOL. SOC. BRAS. MAT., vol. 17 no 2 (1986), pp 67–101.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    R. Roussarie: “Modèles locaux des champs et de formes”. Société Mathématique de France, Astérisque 30, 1975.Google Scholar
  11. [11]
    S. Sternberg: “On the Structure ol local homeomorphism of euclidean n — space III”. American Journal of Math., vol 81 (1959), pp. 578–604.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  1. 1.Laboratoire de Topologie CNRS DO 755Université de BourgogneDijon CedexFrance

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