Dubois, Jean-Guy; Dufour, Jean-Paul; Stanek, Oleg La théorie des catastrophes. IV. Deploiements universels et leurs catastrophes. (French) Zbl 0407.58015 Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. A 24, 261-300 (1976). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 Documents MSC: 58K35 Catastrophe theory Keywords:Local Diffeomorphisms; Infinitesimal Versal Unfoldings; Critical Points; Catastrophe Sets; Multigerm Equivalence Class Citations:Zbl 0293.58004; Zbl 0293.58005 PDFBibTeX XMLCite \textit{J.-G. Dubois} et al., Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. A 24, 261--300 (1976; Zbl 0407.58015) Full Text: Numdam EuDML References: [1] R. Thom , Stabilité structurelle et morphogénèse . Benjamin , Reading, Mass. , 1972 . MR 488155 | Zbl 0294.92001 · Zbl 0294.92001 [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 . MR 246313 | Zbl 0184.48501 · Zbl 0184.48501 [3] R. Thom , Topological models in biology . Topology , vol. 8 , 1969 , p. 313 . MR 245318 | Zbl 0165.23301 · Zbl 0165.23301 [4] R. Thom , Modèles mathématiques de la morphogénèse , chapitre 3. Théorie du déploiement universel , I. H. E. S ., Bures-sur-Yvette , multigr., 1971 . MR 467804 | Zbl 0347.58003 · Zbl 0347.58003 [5] G. Wassermann , Stability of Unfoldings . Lecture Notes in Mathematics , vol. 393 , Springer-Verlag , Berlin , 1974 . MR 410789 | Zbl 0288.57017 · Zbl 0288.57017 [6] J.J. Duistermaat , Oscillatory Integrals, Lagrange Immersions, and Unfoldings of Singularities . Commun. pure appl. Math. , vol. XXVII , no. 2 , 1974 , p. 207 . MR 405513 | Zbl 0285.35010 · Zbl 0285.35010 [7] F. Sergeraert , Un théorème de fonctions implicites sur certains espaces de Fréchet et quelques applications . Ann. scient. Ec. Norm. Sup. , 4 e série, t. 5 , 1972 , p. 599 . Numdam | MR 418140 | Zbl 0246.58006 · Zbl 0246.58006 [8] J.-C. Tougeron , Stabilité des applications différentiables . Séminaire Bourbaki , n^\circ 336 , 1967 , p. 1 . Numdam | Zbl 0209.54901 · Zbl 0209.54901 [9] J.N. Mather , Stability of C\infty mappings. I. The division theorem . Ann. of Math. , no. 87 , 1968 , p. 89 . MR 232401 | Zbl 0159.24902 · Zbl 0159.24902 [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^\circ 2 , 1974 , p. 135 . Numdam | MR 375377 | Zbl 0293.58005 · Zbl 0293.58005 [11] J.N. Mather , Stability of C\infty mappings. III. Finitely determined map-germs . Publ. Math. I. H. E. S. , no. 35 , 1968 , p. 279 . Numdam | MR 275459 | Zbl 0159.25001 · Zbl 0159.25001 [12] D. Siersma , The singularities of C\infty -functions of right-codimension smaller or equal than eight . Indag. Math. , vol. 35 , 1973 , p. 31 . MR 375380 | Zbl 0249.58004 · Zbl 0249.58004 [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 . MR 356124 | Zbl 0278.57011 · Zbl 0278.57011 [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^\circ 5 , 1973 , p. 17 . Zbl 0285.40002 · Zbl 0285.40002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.