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References
Arnol'd, V.I.: Normal forms of functions in neighbourhoods of degenerate critical points. Russian Math. Surveys 29, 10–50 (1974)
Arnol'd, V.I.: Local normal forms of functions. Invent. math.35, 87–109 (1976)
Belitskii, G.R.: Equivalence and normal forms of germs of smooth mappings. Russian Math. Surveys33, 107–177 (1978)
Bochnak, J., Kucharz, W.: Sur les germes d'applications différentiables à singularités isolées. Trans. AMS252, 115–131 (1979)
Gaffney, T.: Properties of finitely-determined germs. Thesis, Brandeis University, 1975
Gaffney, T.: On the order of determination of a finitely-determined germ Invent. Math.37, 83–92 (1976)
Gaffney, T.: A note on the order of determination of a finitely-determined germ. Invent. Math.52, 127–130 (1979)
Gibson, C.G., Wirthmüller, K., du Plessis, A.A., Looijenga, E.J.N.: Topological stability of smooth mappings, Ch. III. Springer LNM 552. Berlin-Heidelberg-New York: Springer-Verlag 1976
Gomozov, E.P.: A versality theorem for a bilateral group of changes of variables. Funct. Anal. Appl.9, 332–333 (1975)
Latour, F.: Stabilité des champs d'applications différentiables; généralisation d'un théorème de J. Mather. Comptes Rendus Acad. Sci.268(A), 1331–1334 (1969)
Martinet, J.: Deplorements versels des applications différentiables et classification des applications stables. In: Singularités d'Applications Différentiables (O. Burlet and F. Ronga, eds.) pp. 144, Springer LNM 535. Berlin-Heidelberg-New York: Springer-Verlag 1976
Martinet, J.: Deploiements stables des germes de type fini, et détermination finie des applications différentiables. Preprint, Université de Strasbourg, 1976
Mather, J.N.: Stability ofC ∞ mappings, III: finitely determined germs. Publ. Math. IHES35, 127–156 (1969)
Mather, J.N.: Stability ofC ∞ mappings, IV: classification of stable germs by ℝ-algebras. Publ. Math. IHES37, 223–248 (1970)
Mather, J.N.: Stability ofC ∞ mappings, VI: the nice dimensions. In: Proc. Liverpool Singularities Symp. I (C.T.C. Wall, ed.). Springer LNM 192. Berlin-Heidelberg-New York: Springer-Verlag 1971
Mather, J.N.: Generic Projections. Ann. of Math.98, 226–245 (1973)
Nirenberg, L.: A proof of the Malgrange Preparation Theorem. In: Proc. Liverpool Singularities Symp. I (C.T.C. Wall, ed.). Springer LNM 192. Berlin-Heidelberg-New York: Springer-Verlag 1971
Siersma, D.: Classification and deformation of singularities. Thesis, University of Amsterdam, 1974
Siersma, D.: Periodicities in Arnol'd's lists of singularities. In: Real and complex singularities, Oslo 1976 (P. Holm, ed.) pp.497–524, Sijthoff & Noordhoff 1977
Wall, C.T.C.: Lectures onC ∞-stability and classification. In: Proc. Liverpool Singularities Symp. I (C.T.C. Wall, ed.). Springer LNM 192. Berlin-Heidelberg-New York: Springer-Verlag 1971
Wall, C.T.C.: Are maps finitely determined in general? Bull. LMS11, 151–154 (1979)
Wassermann, G.: Stability of Unfoldings. Springer LNM 393. Berlin-Heidelberg-New York: Springer-Verlag 1974
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To the memory of my good friend Peter Stefan
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du Plessis, A. On the determinacy of smooth map-germs. Invent Math 58, 107–160 (1980). https://doi.org/10.1007/BF01403166
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DOI: https://doi.org/10.1007/BF01403166