Singularities of envelopes of families of submanifolds in ${ℝ}^N$

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1. [1] V. I. ARNOLD, Wave Front Evolution and Equivariant Morse Lemma (Comm. on Pure and Applied Math., Vol. XXIX, 1976, pp. 557-582). Zbl0343.58003MR55 #9148
2. [2] W. BLASCHKE, Topological Questions of Differential Geometry (Mimmeographed Notes, University of Chicago 1932). 
3. [3] W. BLASCHKE, Geometrie der Gewebe, Springer-Verlag, Balin, 1938. Zbl0020.06701JFM64.0727.03
4. [4] G. E. BREDON, Introduction to Compact Transformation Group, Academic Press, 1972. Zbl0246.57017MR54 #1265
5. [5] V. G. BOLTYANSKII, Envelopes, Pergamon Press, Macmillan, New York, 1964. Zbl0126.37102MR31 #2438
6. [6] M. J. D. CARNEIRO, On the Envelope Theory (Thesis, Princeton University, 1980). 
7. [7] S. CHERN and P. GRIFFITHS, Abel's Theorem and Webs, Jahusbericht der Deutschen Mathematiker Vereinigung, Vol. 80, 1978, pp. 13-110. Zbl0386.14002MR80b:53008
8. [8] J. P. DUFOUR, Diagrammes d'applications differentiables (Thèse, Université du Languedoc, 1979). 
9. [9] J. P. DUFOUR, Sur la stabilité des diagrammes d'applications differentiables, (Ann. scient. Éc. Norm. Sup., 4e série, t. 10, 1977, pp. 153-174). Zbl0354.58011MR56 #6702
10. [10] J. P. DUFOUR, Triplets de fonctions et stabilité des enveloppes, preprint, 1981. Zbl0486.58005MR83j:58019
11. [11] G. GLAESER, Fonctions composées différentiables (Annals of Mathematics, Vol. 77, N° 1, January 1963, pp. 193-208). Zbl0106.31302MR26 #624
12. [12] M. GOLUBITSKY and V. GUILLEMIN, Stable Mappings and Their Singularities, (G.T.M., Springer-Verlag, 1973). Zbl0294.58004MR49 #6269
13. [13] G. JULIA, Cours de géometrie infinitesimal, Gauthier-Villars, Paris, 1953. 
14. [14] J. N. MATHER, Stability of C∞ Mappings II : Infinitesimal Stability Implies Stability (Ann. Math., Vol. 89, 1969, pp. 254-291). Zbl0177.26002MR41 #4582
15. [15] J. N. MATHER, Stability of C∞ Mappings III : Finitely Determined Map Germs (I.H.E.S., Publications Mathematiques, No. 35, 1968). Zbl0159.25001MR43 #1215a
16. [16] V. PŒNARU, Singularities C∞ in Presence de Symmetrie, Springer-Verlag (Lecture Notes, Berlin, 1976). 
17. [17] S. STERNBERG, Local Cn Transformations of the Real Line (Duke Math. J., Vol. 24, 1957, pp. 97-112). Zbl0077.06201MR21 #1371
18. [18] R. THOM, Sur la theorie des enveloppes (J. Math. pure et appl. T. XLI, fasc. 2, 1962). Zbl0105.16102MR25 #4454

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