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Transformation of germs of differentiable functions through changes of local coordinates. (English) Zbl 0271.58003


MSC:

58C05 Real-valued functions on manifolds
26E10 \(C^\infty\)-functions, quasi-analytic functions
26B10 Implicit function theorems, Jacobians, transformations with several variables
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[1] Artin, M., On the solution of analytic equations, Inventions Math., 5 (1968), 277-291. · Zbl 0172.05301
[2] Cerf, J., La stratification naturelle des espaces de fonctions differentiables reel- les et le theoreme de la pseudoisotopie, Publ. Math. I.H.E.S., 39 (1970). · Zbl 0213.25202
[3] Levinson, N., A canonical form for an analytic function of several variables at a critical point, Bull. Amer. Math. Soc., 66 (1960) 68-69. · Zbl 0192.18201
[4] Levinson, N., A polynomial canonical form for certain analytic functions of two variables at a critical point, Bull. Amer. Math. Soc., 66 (1960) 366-368. · Zbl 0192.18202
[5] Lojasiewicz, S., Ensembles semi-analytiques, Cours Faculte des Sciences d’Orsay Momeographie I.H.E.S., Buressur-Yvette, July, 1965.
[6] Malgrange, B., Ideals of differentiable functions, Oxford University Press, 1966. · Zbl 0177.17902
[7] Mather, J., Stability of C^\circ ^\circ mappings; III Finitely determined map germs, Publ. Math. I.H.E.S., 35 (1968), 127-156. · Zbl 0159.25001
[8] Tougeron, J. Cl., Ideaux de fonctions differentiable, 1. Ann. Inst. Fourier, 18, 1 (1968) 177-240.
[9] Whitney, H., Local properties of analytic varieties, M. Morse Jubilee Volume, Differential anp Combinatorial Topology, Princeton Univ. Press, 1965, p. 205-244. Department of Mathematics, Kyoto University. · Zbl 0129.39402
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