Bifurcations de polycycles infinis pour les champs de vecteurs polynomiaux du plan

Mohamed El Morsalani

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

  • Volume: 3, Issue: 3, page 387-410
  • ISSN: 0240-2963

How to cite

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El Morsalani, Mohamed. "Bifurcations de polycycles infinis pour les champs de vecteurs polynomiaux du plan." Annales de la Faculté des sciences de Toulouse : Mathématiques 3.3 (1994): 387-410. <http://eudml.org/doc/73341>.

@article{ElMorsalani1994,
author = {El Morsalani, Mohamed},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {polycycles; Hilbert's 16th problem; differentiable vector fields on the plane; finite cyclicity},
language = {fre},
number = {3},
pages = {387-410},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Bifurcations de polycycles infinis pour les champs de vecteurs polynomiaux du plan},
url = {http://eudml.org/doc/73341},
volume = {3},
year = {1994},
}

TY - JOUR
AU - El Morsalani, Mohamed
TI - Bifurcations de polycycles infinis pour les champs de vecteurs polynomiaux du plan
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1994
PB - UNIVERSITE PAUL SABATIER
VL - 3
IS - 3
SP - 387
EP - 410
LA - fre
KW - polycycles; Hilbert's 16th problem; differentiable vector fields on the plane; finite cyclicity
UR - http://eudml.org/doc/73341
ER -

References

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  1. [C] Cherkas ( L.A.) .— Structure of a successor function in the neighborhood of a separatrix of a perturbed analytic autonomous system in the plane, Translated From Differentsial'nye Uravneniya17, n° 3, (March 1981), pp. 469-478. Zbl0503.34019MR610508
  2. [DRR] Dumortier ( F.), Roussarie ( R.) et Rousseau ( C.) .— The 16th problem of Hilbert in quadratic fields, Preprint (1991). 
  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. [M1] Mourtada ( A.) .— Cyclicité finie des polycycles hyperboliques de champs de vecteurs du plan. Mise sous forme normale, L.N.M.Proceeding Luminy 1989 (Bifurcations of planar vector fields), ed. J.-P. Françoise et R. Roussarie 1445 (1989), pp. 272-314. Zbl0719.58031MR1094384
  5. [M] Mourtada ( A.) .— Polycycles hyperboliques dégénérés et non triviaux à deux sommets, à paraître dans J. Differential Equations. 
  6. [R1] Roussarie ( R.) . — A note on finite cyclicity property and Hilbert's 16th problem, Dynamical systems, (proc. Chilean Symp. Valparaiso, 1986), L.N.M., ed. R. Bamon, R. Labarca and J. Palis Jr., Berlinspringer1331 (1988), pp. 161-168. Zbl0676.58046MR961099
  7. [R2] Roussarie ( R.) . — On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields, Bol. Soc. Mat.17, n° 2 (1986), pp. 67-101. Zbl0628.34032MR901596
  8. [R3] Roussarie ( R.) . — Cyclicité finie des lacets et des points cuspidaux, Nonlinearity2 (1989), pp. 73-117. Zbl0679.58037MR980858
  9. [S] Sternberg ( S.) .— On the structure of local homeomorphisms of euclidean n-space III, American Journal of Math.81 (1959), pp. 578-604. Zbl0211.56304MR109853

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