Shiota, Masahiro Transformation of germs of differentiable functions through changes of local coordinates. (English) Zbl 0271.58003 Publ. Res. Inst. Math. Sci., Kyoto Univ. 9, 123-140 (1973). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 Documents MSC: 58C05 Real-valued functions on manifolds 26E10 \(C^\infty\)-functions, quasi-analytic functions 26B10 Implicit function theorems, Jacobians, transformations with several variables PDFBibTeX XMLCite \textit{M. Shiota}, Publ. Res. Inst. Math. Sci. 9, 123--140 (1973; Zbl 0271.58003) Full Text: DOI References: [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 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.