ArticleOriginal scientific text

Title

Birkhoff normal formsand analytic geometry

Authors 1

Affiliations

  1. Département de Mathématiques, Université de Paris VI, BP 172 4, Place Jussieu, tour 46-45, 5e étage, 75252 Paris, France

Bibliography

  1. [A] M. Artin, On the solutions of analytic equations, Invent. Math. 5 (1968), 277-291.
  2. [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, Amer. Math. Soc. Transl. Ser. 1, 5 (1962), 336-413. Translated from: Mat. Sbornik N.S. 30 (1952), 181-196.
  3. [D] H. Dulac, Détermination et intégration d'une certaine classe d'équations différentielles ayant pour point singulier un centre, Bull. Sci. Math. 32 (1908), 230-252.
  4. [F-P] J. P. Françoise and C. C. Pugh, Keeping track of limit cycles, J. Differential Equations 65 (1986), 139-157.
  5. [F-Po] J. P. Françoise et R. Pons, Une approche algorithmique du problème du centre pour des perturbations homogènes, Bull. Sci. Math. 120 (1996), 1-17.
  6. [Ga] A. M. Gabrielov, Formal relations between analytic functions, Funct. Anal. Appl. 5 (1971), 64-65.
  7. [G] V. Guillemin, The Radon transform on Zoll surfaces, Adv. Math. 22 (1976), 85-119.
  8. [M] B. Malgrange, Frobenius à singularité I, codimension un, Inst. Hautes Études Sci. Publ. Math. 46 (1976), 163-174.
  9. [P] A. Płoski, Note on a theorem of M. Artin, Bull. Polish Acad. Sci. Math. 22 (1974), 1107-1109.
  10. [S] C. L. Siegel, Über die Existenz einer Normalform analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtlösung, Math. Ann. 128 (1954), 144-170.
  11. [V] J. Vey, Sur certains systèmes dynamiques séparables, Amer. J. Math. 100 (1978), 591-614.
  12. [Z1] H. Żołądek, Quadratic systems with center and their perturbations, J. Differential Equations 109 (1994), 223-273.
  13. [Z2] H. Żołądek, On a certain generalization of Bautin's theorem, Nonlinearity 7 (1994), 273-280.
Pages:
49-56
Main language of publication
English
Published
1997
Exact and natural sciences