Bifurcation de cycles limites au voisinage de polycycles hyperboliques et génériques à trois sommets

Abderaouf Mourtada

Annales de la Faculté des sciences de Toulouse : Mathématiques (1994)

  • Volume: 3, Issue: 2, page 259-292
  • ISSN: 0240-2963

How to cite

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Mourtada, Abderaouf. "Bifurcation de cycles limites au voisinage de polycycles hyperboliques et génériques à trois sommets." Annales de la Faculté des sciences de Toulouse : Mathématiques 3.2 (1994): 259-292. <http://eudml.org/doc/73335>.

@article{Mourtada1994,
author = {Mourtada, Abderaouf},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {bifurcation; 16th Hilbert problem; limit cycles; hyperbolic polycycles},
language = {fre},
number = {2},
pages = {259-292},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Bifurcation de cycles limites au voisinage de polycycles hyperboliques et génériques à trois sommets},
url = {http://eudml.org/doc/73335},
volume = {3},
year = {1994},
}

TY - JOUR
AU - Mourtada, Abderaouf
TI - Bifurcation de cycles limites au voisinage de polycycles hyperboliques et génériques à trois sommets
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1994
PB - UNIVERSITE PAUL SABATIER
VL - 3
IS - 2
SP - 259
EP - 292
LA - fre
KW - bifurcation; 16th Hilbert problem; limit cycles; hyperbolic polycycles
UR - http://eudml.org/doc/73335
ER -

References

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  1. [B] Bautin ( N.) .— 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, Mat. Sb. (N.S.)30, n° 72 (1952), pp. 181-196. Zbl0059.08201MR45893
  2. [EMMR] Ecalle ( J.), Martinet ( J.), Moussu ( R.) et Ramis ( J.-P.) .— Non-accumulation de cycles limites, C.R.A.S., t. 304, Série I, 14 (1987), (I) pp. 375-378 et (II) pp. 431-434. Zbl0615.58011MR888240
  3. [FP] Françoise ( J.-P.) et Pugh ( C.C.) .— Keeping track of limit cycles, Journal of Diff. Eq.65 (1986), pp. 139-157. Zbl0602.34019MR861513
  4. [I] IL'YASHENKO ( Yu) .— Ycπ, Man. Hayk.42, n° 3 (1987), pp. 223. 
  5. [J] Joyal ( P.) .— Generalized Hopf bifurcation and its dual : generalized homoclinic bifurcation, S.I.A.M. J. of Applied Mathematics (1988). Zbl0642.34041MR941096
  6. [M1] Mourtada ( A.) .— Cyclicité finie des polycycles hyperboliques de champs de vecteurs du plan. Mise sous forme normale, L.N.M., Proceeding Luminy (Bifurcations of planar vector fields), Éd. J.-P. Françoise et R. Roussarie 1455 (1989), pp. 272-314. Zbl0719.58031MR1094384
  7. [M2] Mourtada ( A.) .— Cyclicité finie des polycycles des hyperboliques de champs de vecteurs du plan. Algorithme de finitide, Ann. Inst. Fourier Grenoble43, n° 3 (1991), pp. 719-753. Zbl0725.58032MR1136601
  8. [M3] Mourtada ( A.) .— Bifurcations de cycles limites au voisinage de polycycles hyperboliques et génériques à quatre sommets, Preprint Dijon (1992). 
  9. [R1] Roussarie ( R.) . — A note on finite cyclicity property and Hilbet's 16th problem, Dynamical System (Proc. Chilean Symp. Valparaiso 1986), L.N.M.1331, R. Barmon, R. Labarca and J. Palis Jr ( ed.), Berlin, Springer (1988), pp. 161-168. Zbl0676.58046MR961099
  10. [R2] Roussarie ( R.) . — On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields, Bol. Soc. Bras. Mat.17, n° 2 (1986), pp. 67-101. Zbl0628.34032MR901596

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