Champs lents-rapides complexes à une dimension lente

Jean-Louis Callot

Annales scientifiques de l'École Normale Supérieure (1993)

  • Volume: 26, Issue: 2, page 149-173
  • ISSN: 0012-9593

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Callot, Jean-Louis. "Champs lents-rapides complexes à une dimension lente." Annales scientifiques de l'École Normale Supérieure 26.2 (1993): 149-173. <http://eudml.org/doc/82338>.

@article{Callot1993,
author = {Callot, Jean-Louis},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {slow-fast vector field with one slow dimension; complex foliation; delayed bifurcation phenomenon; irregular singularity; linear differential equation; equations of Bessel and Airy},
language = {fre},
number = {2},
pages = {149-173},
publisher = {Elsevier},
title = {Champs lents-rapides complexes à une dimension lente},
url = {http://eudml.org/doc/82338},
volume = {26},
year = {1993},
}

TY - JOUR
AU - Callot, Jean-Louis
TI - Champs lents-rapides complexes à une dimension lente
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1993
PB - Elsevier
VL - 26
IS - 2
SP - 149
EP - 173
LA - fre
KW - slow-fast vector field with one slow dimension; complex foliation; delayed bifurcation phenomenon; irregular singularity; linear differential equation; equations of Bessel and Airy
UR - http://eudml.org/doc/82338
ER -

References

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  1. [1] E. BENOÎT, Équation de van der Pol avec terme forçant (Thèse de troisième cycle, Paris, 1979). 
  2. [2] E. BENOÎT, J.-L. CALLOT, F. DIENER et M. DIENER, Chasse au canard (Collectanea Mathematica, Barcelone, 31, 1981, p. 37-119). Zbl0529.34046MR85g:58062a
  3. [3] I. P. VAN DEN BERG, Non standard asymptotic analysis, Springer, Berlin, Heidelberg, New York, 1987. Zbl0633.41001MR89g:03097
  4. [4] B. CANDELPERGHER, F. DIENER et M. DIENER, Retard à la bifurcation : du local au global, in Bifurcations of planar vector fields, J. P. FRANÇOISE et R. ROUSSOIR éd., Springer, 1990, p. 1-19. Zbl0739.34021MR92k:58188
  5. [5] F. DIENER et G. REEB, Analyse non standard, Hermann, Paris, 1989. Zbl0682.26010MR91k:03157
  6. [6] M. DIENER et G. REEB, Champs polynomiaux : nouvelles trajectoires remarquables (Bull. Soc. Math. Belgique, 38, 1987, p. 131-150). Zbl0681.34034MR88d:58096
  7. [7] C. LOBRY et G. WALLET, La traversée de l'axe imaginaire n'a pas toujours lieu là où l'on croit l'observer, in Mathématiques finitaires et analyse non standard, M. DIENER et G. WALLET éd. (Publications Mathématiques de l'Université Paris-VII, 1, 31, 1989, p. 45-51). Zbl0687.58029MR1028789
  8. [8] R. LUTZ et M. GOZE, Non standard analysis : a practical guide with applications, Springer, Berlin, Heidelberg, New York, 1981. Zbl0506.03021
  9. [9] E. NELSON, Internal Set Theory (Bull. Amer. Math. Soc., 83, 6, 1977, p. 1165-1198). Zbl0373.02040MR57 #9544
  10. [10] A. I. NEISHTADT, Persistence of stability loss for dynamical bifurcations, 1 (Differentsial'nye Uravneniya (Differential Equations), 23, (12), 1987, (88), p. 2060-2067 (1385-1390)). Zbl0716.34064MR89f:34074
  11. [11] A. I. NEISHTADT, Persistence of stability loss for dynamical bifurcations, 2 (Differentsial'nye Uravneniya (Differential Equations), 24, (12), 1988, (88), p. 226-233 (171-176)). Zbl0677.58035MR90a:34107
  12. [12] A. ROBINSON, Non standard analysis, North Holland, 1974. 
  13. [13] M. A. SHISHKOVA, Examination of a system of differential equations with a small parameter in the highest derivatives (Dokl. Akad. Nauk SSSR, 209, 3, 1973, p. 576-579). Zbl0289.34083

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