Birkhoff normal formsand analytic geometry

Jean Françoise

Banach Center Publications (1997)

  • Volume: 39, Issue: 1, page 49-56
  • ISSN: 0137-6934

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Françoise, Jean. "Birkhoff normal formsand analytic geometry." Banach Center Publications 39.1 (1997): 49-56. <http://eudml.org/doc/208678>.

@article{Françoise1997,
author = {Françoise, Jean},
journal = {Banach Center Publications},
keywords = {analytic vector field; normal form; Hamiltonian system; center problem},
language = {eng},
number = {1},
pages = {49-56},
title = {Birkhoff normal formsand analytic geometry},
url = {http://eudml.org/doc/208678},
volume = {39},
year = {1997},
}

TY - JOUR
AU - Françoise, Jean
TI - Birkhoff normal formsand analytic geometry
JO - Banach Center Publications
PY - 1997
VL - 39
IS - 1
SP - 49
EP - 56
LA - eng
KW - analytic vector field; normal form; Hamiltonian system; center problem
UR - http://eudml.org/doc/208678
ER -

References

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  1. [A] M. Artin, On the solutions of analytic equations, Invent. Math. 5 (1968), 277-291. Zbl0172.05301
  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. Zbl0059.08201
  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. Zbl39.0374.01
  4. [F-P] J. P. Françoise and C. C. Pugh, Keeping track of limit cycles, J. Differential Equations 65 (1986), 139-157. Zbl0602.34019
  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. Zbl0353.53027
  8. [M] B. Malgrange, Frobenius à singularité I, codimension un, Inst. Hautes Études Sci. Publ. Math. 46 (1976), 163-174. Zbl0355.32013
  9. [P] A. Płoski, Note on a theorem of M. Artin, Bull. Polish Acad. Sci. Math. 22 (1974), 1107-1109. Zbl0302.32002
  10. [S] C. L. Siegel, Über die Existenz einer Normalform analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtlösung, Math. Ann. 128 (1954), 144-170. Zbl0057.32002
  11. [V] J. Vey, Sur certains systèmes dynamiques séparables, Amer. J. Math. 100 (1978), 591-614. Zbl0384.58012
  12. [Z1] H. Żołądek, Quadratic systems with center and their perturbations, J. Differential Equations 109 (1994), 223-273. Zbl0797.34044
  13. [Z2] H. Żołądek, On a certain generalization of Bautin's theorem, Nonlinearity 7 (1994), 273-280. Zbl0838.34035

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