La théorie des catastrophes. IV. Déploiements universels et leurs catastrophes

Jean-Guy Dubois; Jean-Paul Dufour; Oleg Stanek

Annales de l'I.H.P. Physique théorique (1976)

  • Volume: 24, Issue: 3, page 261-300
  • ISSN: 0246-0211

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Dubois, Jean-Guy, Dufour, Jean-Paul, and Stanek, Oleg. "La théorie des catastrophes. IV. Déploiements universels et leurs catastrophes." Annales de l'I.H.P. Physique théorique 24.3 (1976): 261-300. <http://eudml.org/doc/75897>.

@article{Dubois1976,
author = {Dubois, Jean-Guy, Dufour, Jean-Paul, Stanek, Oleg},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Local Diffeomorphisms; Infinitesimal Versal Unfoldings; Critical Points; Catastrophe Sets; Multigerm Equivalence Class},
language = {fre},
number = {3},
pages = {261-300},
publisher = {Gauthier-Villars},
title = {La théorie des catastrophes. IV. Déploiements universels et leurs catastrophes},
url = {http://eudml.org/doc/75897},
volume = {24},
year = {1976},
}

TY - JOUR
AU - Dubois, Jean-Guy
AU - Dufour, Jean-Paul
AU - Stanek, Oleg
TI - La théorie des catastrophes. IV. Déploiements universels et leurs catastrophes
JO - Annales de l'I.H.P. Physique théorique
PY - 1976
PB - Gauthier-Villars
VL - 24
IS - 3
SP - 261
EP - 300
LA - fre
KW - Local Diffeomorphisms; Infinitesimal Versal Unfoldings; Critical Points; Catastrophe Sets; Multigerm Equivalence Class
UR - http://eudml.org/doc/75897
ER -

References

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  2. [2] F. Latour, Stabilité des champs d'applications différentiables ; généralisation d'un théorème de J. Mather. C. R. Acad. Sci. Paris, t. 268, 1969, p. 1331. Zbl0184.48501MR246313
  3. [3] R. Thom, Topological models in biology. Topology, vol. 8, 1969, p. 313. Zbl0165.23301MR245318
  4. [4] R. Thom, Modèles mathématiques de la morphogénèse, chapitre 3. Théorie du déploiement universel, I. H. E. S., Bures-sur-Yvette, multigr., 1971. Zbl0347.58003MR467804
  5. [5] G. Wassermann, Stability of Unfoldings. Lecture Notes in Mathematics, vol. 393, Springer-Verlag, Berlin, 1974. Zbl0288.57017MR410789
  6. [6] J.J. Duistermaat, Oscillatory Integrals, Lagrange Immersions, and Unfoldings of Singularities. Commun. pure appl. Math., vol. XXVII, no. 2, 1974, p. 207. Zbl0285.35010MR405513
  7. [7] F. Sergeraert, Un théorème de fonctions implicites sur certains espaces de Fréchet et quelques applications. Ann. scient. Ec. Norm. Sup., 4e série, t. 5, 1972, p. 599. Zbl0246.58006MR418140
  8. [8] J.-C. Tougeron, Stabilité des applications différentiables. Séminaire Bourbaki, n° 336, 1967, p. 1. Zbl0209.54901
  9. [9] J.N. Mather, Stability of C∞ mappings. I. The division theorem. Ann. of Math., no. 87, 1968, p. 89. Zbl0159.24902MR232401
  10. [10] J.-G. Dubois et J.-P. Dufour, La théorie des catastrophes. II. Dynamiques gradientes à une variable d'état. Ann. Inst. Henri Poincaré, Section A, vol. XX, n° 2, 1974, p. 135. Zbl0293.58005MR375377
  11. [11] J.N. Mather, Stability of C∞ mappings. III. Finitely determined map-germs. Publ. Math. I. H. E. S., no. 35, 1968, p. 279. Zbl0159.25001MR275459
  12. [12] D. Siersma, The singularities of C∞-functions of right-codimension smaller or equal than eight. Indag. Math., vol. 35, 1973, p. 31. Zbl0249.58004MR375380
  13. [13] V.I. Arnol'd, Normal forms for functions near degenerate critical points, the Weyl groups of Ak, Dk, Ek and Lagrangian singularities. Funct. Anal. and its Appl., vol. 6, no. 4, 1972, p. 254. Zbl0278.57011MR356124
  14. [14] V.I. Arnol'd, Remarques sur la méthode de la phase stationnaire et les nombres de Coxeter (en russe). Uspekhi Mat. Nauk, t. XXVIII, n° 5, 1973, p. 17. Zbl0285.40002

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