Canards et enlacements

E. Benoît

Publications Mathématiques de l'IHÉS (1990)

  • Volume: 72, page 63-91
  • ISSN: 0073-8301

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Benoît, E.. "Canards et enlacements." Publications Mathématiques de l'IHÉS 72 (1990): 63-91. <http://eudml.org/doc/104072>.

@article{Benoît1990,
author = {Benoît, E.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {pseudo-singular point; singular Riccati's equation; non-standard analysis; phase portraits; duck-shaped solutions; singular perturbation problem; slow surface; generic fold; number of jumps; winding number; constrained equation; numerical results},
language = {fre},
pages = {63-91},
publisher = {Institut des Hautes Études Scientifiques},
title = {Canards et enlacements},
url = {http://eudml.org/doc/104072},
volume = {72},
year = {1990},
}

TY - JOUR
AU - Benoît, E.
TI - Canards et enlacements
JO - Publications Mathématiques de l'IHÉS
PY - 1990
PB - Institut des Hautes Études Scientifiques
VL - 72
SP - 63
EP - 91
LA - fre
KW - pseudo-singular point; singular Riccati's equation; non-standard analysis; phase portraits; duck-shaped solutions; singular perturbation problem; slow surface; generic fold; number of jumps; winding number; constrained equation; numerical results
UR - http://eudml.org/doc/104072
ER -

References

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  1. [1] J. ARGEMI, Approche qualitative d'un problème de perturbations singulières dans R4, in Equadiff 1978, éd. R. Conti, G. Sestini, G. Villari, 333-340. Zbl0432.92011
  2. [2] E. BENOÎT, Systèmes lents-rapides dans R3 et leurs canards, in Troisième Rencontre du Schnepfenried, Astérisque, 109/110 (1983), 159-191. Zbl0529.34037MR86d:58103
  3. [3] I. P. VAN DEN BERG, Un principe de permanence général, in Troisième Rencontre du Schnepfenried, Astérisque, 109/110 (1983), 193-223. Zbl0548.03039MR86e:03061
  4. [4] J.-L. CALLOT, Bifurcation du portrait de phase pour des équations différentielles linéaires du second ordre ayant pour type l'équation d'Hermite, thèse d'Etat, Strasbourg, 1981. 
  5. [5] F. DIENER, Cours d'analyse non standard, Alger, Office des Publications universitaires, 1983. 
  6. [6] F. DIENER et G. REEB, Analyse non standard, Paris, Hermann, 1989. Zbl0682.26010MR91k:03157
  7. [7] M. DIENER, Canards et bifurcations, in Outils et modèles mathématiques pour l'automatique, l'analyse des systèmes et le traitement du signal, vol. 3, Publication du CNRS (1983), 289-313. MR783843
  8. [8] M. DIENER et I. P. VAN DER BERG, Halos et galaxies, une extension du lemme de Robinson, Comptes rendus de l'Académie des Sciences de Paris, 293 (1981), 385-388. MR82m:03071
  9. [9] N. LEVINSON, Perturbations of discontinuous solutions of non-linear systems of differential equations, Acta Mathematica, 82 (1950), 71-106. Zbl0039.31404MR11,722b
  10. [10] A. I. NEISHTADT, Persistence of stability loss for dynamical bifurcations, Differential'nye Uravneniya, 23 (12), (1987), 2060-2067. Zbl0716.34064MR89f:34074
  11. [11] E. NELSON, Internal Set Theory, Bull. Amer. Math. Soc., 83 (1977), 1165-1198. Zbl0373.02040MR57 #9544
  12. [12] A. ROBINSON, Non standard Analysis, Amsterdam, North Holland, 1966. Zbl0151.00803MR34 #5680
  13. [13] F. TAKENS, Constrained equations, a study of implicit differential equations and their discontinuous solutions, in Structural stability, the theory of catastrophes and applications in the sciences, Springer Lecture Notes in Math., 525 (1976), 143-234. Zbl0386.34003
  14. [14] A. TIHONOV, On the dependence of the solutions of differential equations on a small parameter, Math. Sbornik, 22 (1948), 193-204. MR9,588e
  15. [15] G. WALLET, Entrée-sortie dans un tourbillon, Ann. Inst. Fourier, 36-4 (1986), 157-184. Zbl0593.76032MR88h:34032

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