A note on finite cyclicity property and Hilbert's 16th. Problem

  • R. Roussarie
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1331)


Periodic Orbit Singular Point Cusp Point Elliptic Point Hyperbolic Saddle 
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  1. [B]
    N. Bautin., On the number of limit cycles appearing with variations of the coefficients from an equilibrium state of the type of a focus or a center, Math. Sb. (N.S.) 30 (72) (1952), p. 181–196.MathSciNetGoogle Scholar
  2. [EMMR 1,2]
    J. Ecalle., J. Martinet., R. Moussu., J.P. Ramis., Non-accumulation de cycles limites, C.R.A.S., t. 304, série I, no 14 (1987), (I): p. 375–378, (II): p. 431–434.Google Scholar
  3. [F.P.]
    J.P. Francoise and C.C. Pugh., Keeping track of limit cycles, Journal of Diff. Eq. 65 (1986) p. 139–157.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [I]
    Yu. Il'yasenko., Ycπ. Math. Hayk., 42, 3 (1987), p. 223.Google Scholar
  5. [K]
    K. Kuratowski., Topology, Vol. II, Academic Press, N.Y. London (1966).zbMATHGoogle Scholar
  6. [R1]
    [R1] R. Roussarie., On the number of limit cycles which appear by perturbation of a separatrix loop of planar vector fields. Bol. Soc. Math. Bras. Vol. 17, no 2 (1986) p. 67–101.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [R2]
    [R2] R. Roussarie., Déformations génériques des cusps. (To appear in Astérisque: Journées Singulieres, Dijon, 1985).Google Scholar
  8. [R3]
    [R3] R. Roussarie., Cyclicité finie des lacets et des points cuspidaux. (Preprint)Google Scholar
  9. [Y]
    J. Ch. Yoccoz., Non-accumulation des cycles limites, Séminaire Bourbaki 40e. Année, 1987–88, no 690.Google Scholar

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© Springer-Verlag 1988

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  • R. Roussarie

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