Shiota, Masahiro Equivalence of differentiable functions, rational functions and polynomials. (English) Zbl 0466.58006 Ann. Inst. Fourier 32, No. 4, 167-204 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 Documents MSC: 58C05 Real-valued functions on manifolds 58C25 Differentiable maps on manifolds 58K99 Theory of singularities and catastrophe theory Keywords:equivalence to a polynomial; number of critical points; Milnor number of the germ at each critical point; locally equivalent to a germ of a rational function; real affine non-singular algebraic varieties; right equivalence of smooth functions PDFBibTeX XMLCite \textit{M. Shiota}, Ann. Inst. Fourier 32, No. 4, 167--204 (1982; Zbl 0466.58006) Full Text: DOI Numdam EuDML References: [1] [1] , Ensemble semi-algebraic, IHES, 1965. [2] [2] , Lectures on the h-cobordism theorem, Princeton U.P., 1965. · Zbl 0161.20302 [3] [6] , Abelian varieties, Oxford Univ., Press 1970. · Zbl 0223.14022 [4] [4] , Equivalence of differentiable mappings and analytic mappings, Publ. Math. IHES, 54 (1981), 37-122. · Zbl 0516.58012 [5] [5] , On the unique factorial property of the ring of Nash functions, Publ. RIMS, Kyoto Univ., 17 (1981), 363-369. · Zbl 0503.58001 [6] [6] , Sur la factorialité de l’anneau des fonctions lisses rationnelles, C.R., A.S., Paris, 282 (1981), 67-70. · Zbl 0489.14013 [7] [7] , , Sur la clôture intégrale d’un idéal de germes de fonctions holomorphes en un point de Cn, C.R.A.S., Paris, 278 (1974), 949-951. · Zbl 0307.32007 [8] [8] , Differentiable and combinatorial structures on manifolds, Ann. of Math., 74 (1961), 498-502. · Zbl 0111.18902 [9] [9] , L’équivalence d’une fonction différentiable et d’un polynôme, Topology, 3., Suppl. 2 (1965), 297-307. · Zbl 0133.30702 [10] [10] , Algebraic geometry and Nash functions, Academic Press, 1978. · Zbl 0418.14002 [11] [11] , Idéaux de fonctions différentiables I, Ann. Ins. Fourier, 18 (1968), 177-240. · Zbl 0188.45102 [12] [12] , A certain region in Euclidean 3-space, Proc. Nat. Acad. Sci., 21 (1935), 364-366. · Zbl 0012.03604 [13] [13] , On irreducible 3-manifolds which are sufficiently large, Ann. of Math., 87 (1968), 56-88. · Zbl 0157.30603 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.