Equivalence of differentiable mappings and analytic mappings
Publications Mathématiques de l'IHÉS, Tome 54 (1981), pp. 37-122. 
@article{PMIHES_1981__54__37_0,
     author = {Shiota, Masahiro},
     title = {Equivalence of differentiable mappings and analytic mappings},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {37--122},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {54},
     year = {1981},
     mrnumber = {84k:58039},
     zbl = {0516.58012},
     language = {en},
     url = {http://archive.numdam.org/item/PMIHES_1981__54__37_0/}
}
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Shiota, Masahiro. Equivalence of differentiable mappings and analytic mappings. Publications Mathématiques de l'IHÉS, Tome 54 (1981), pp. 37-122. http://archive.numdam.org/item/PMIHES_1981__54__37_0/

[1] M. Artin, On the solution of analytic equations, Inv. Math., 5 (1968), 277-291. | MR | Zbl

[2] J. Bochnak-S. Łojasiewicz, A converse of the Kuiper-Kuo Theorem, Lecture Notes in Math., Springer, 192 (1971), 254-261. | MR | Zbl

[3] N. M. Christenson, Zur Łojasiewicz-Ungleichung für differenzierbare Funktionen, Manuscripta Math., 20 (1977), 255-262. | Zbl

[4] M. Hervé, Several complex variables, Local theory, Oxford, 1963. | MR | Zbl

[5] M. W. Hirsch, B. C. Mazur, Smoothings of piecewise linear manifolds, Ann. Math. Studies, 80, Princeton Univ. Press, 1974. | MR | Zbl

[6] L. Hörmander, Linear partial differential operators, Springer, 1969.

[7] H. C. King, Real analytic germs and their varieties at isolated singularities, Inv. Math., 37 (1976), 193-199. | MR | Zbl

[8] R. C. Kirby-L. C. Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulation, Ann. Math. Studies, 88, Princeton Univ. Press, 1977. | MR | Zbl

[9] T. C. Kuo, The jet space Jr(n, p), Lecture Notes in Math., Springer, 192 (1971), 169-177. | MR | Zbl

[10] N. Levinson, A canonical form for an analytic function of several variables at a critical point, Bull. Amer. Math. Soc., 66 (1960), 68-69. | MR | Zbl

[11] N. Levinson, A polynomial canonical form for certain analytic functions of two variables at a critical point, Bull. Amer. Math. Soc., 66 (1960), 366-368. | MR | Zbl

[12] B. Malgrange, Ideals of differentiable functions, Oxford Univ. Press, 1966. | Zbl

[13] B. Malgrange, Sur les points singuliers des équations différentielles, Séminaire Goulaouic-Schwartz, 1972. | Numdam | MR | Zbl

[14] J. N. Mather, How to stratify mapping and jet spaces, Lecture Notes in Math., Springer, 535 (1975), 128-176. | MR | Zbl

[15] J. N. Mather, Stability of C∞ mappings, III. Finitely determined map germs, Publ. Math. I.H.E.S., 35 (1968), 127-156. | Numdam | MR | Zbl

[16] E. E. Moise, Affine structures in 3-manifolds V. The triangulation theorem and Hauptvermutung, Ann. Math., 56 (1952), 96-114. | MR | Zbl

[17] E. E. Moise, Geometric topology in dimension 2 and 3, GTM, Springer, 1977. | MR | Zbl

[18] J. R. Munkres, Obstructions to the smoothing of piecewise differentiable structures, Ann. Math., 72 (1960), 521-554. | MR | Zbl

[19] J. R. Munkres, Obstructions to imposing differentiable structures, Illinois J. Math., 8 (1964), 361-376. | MR | Zbl

[20] M. Nagata, Local rings, John Wiley, 1962. | MR | Zbl

[21] R. Palais, Equivariant real algebraic differential topology, Part I. Smoothness categories and Nash manifolds, Notes Brandeis Univ., 1972. | Zbl

[22] K. Reichard, Nichtdifferenzierbare Morphismen differenzierbarer Räume, Manuscripta Math., 15 (1975), 243-250. | MR | Zbl

[23] J. J. Risler, Le théorème des zéros pour les idéaux de fonctions différentiables en dimension 2 et 3, Ann. Inst. Fourier, Grenoble, 26 (1976), 73-107. | Numdam | MR | Zbl

[24] M. Shiota, Differentiable functions equivalent to analytic functions, Publ. RIMS, Kyoto Univ., 9 (1973), 113-121. | MR | Zbl

[25] M. Shiota, Transformations of germs of differentiable functions through changes of local coordinates, Publ. RIMS, Kyoto Univ., 9 (1973), 123-140. | MR | Zbl

[26] M. Shiota, On germs of differentiable functions in two variables, Publ. RIMS, Kyoto Univ., 9 (1974), 319-324. | MR | Zbl

[27] M. Shiota, Some results on formal power series and differentiable functions, Publ. RIMS, Kyoto Univ., 12 (1976), 49-53. | MR | Zbl

[28] M. Shiota, Thesis, Univ. of Rennes, France, 1978.

[29] L. C. Siebenmann, Deformation of homeomorphisms on stratified sets, Comm. Math. Helv, 47 (1972), 123-163. | MR | Zbl

[30] H. Skoda, J. Briançon, Sur la clôture intégrale d'un idéal de germes de fonctions holomorphes en un point de Cn, C.R. Acad. Sc. Paris, 278 (1974), 949-951. | MR | Zbl

[31] J. C. Tougeron, Idéaux de fonctions différentiables I, Ann. Inst. Fourier, 18 (1968), 177-240. | Numdam | MR | Zbl

[32] M. Van Der Put, Some properties of the ring of germs of C∞ functions, Compositio Math., 34 (1977), 99-108. | Numdam | MR | Zbl

[33] H. Whitney, A function not constant on a connected set of critical points, Duke Math. J., 1 (1935), 514-517. | JFM | Zbl

[34] H. Whitney, Local properties of analytic varieties, Differential and Combinatorial topology, Princeton Univ. Press, 1965, 205-244. | MR | Zbl

[35] H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc., 36 (1934), 63-89. | JFM | MR | Zbl

[36] G. T. Whyburn, Analytic topology, Amer. Math. Soc. Colloq. Publ., 28, 1942. | MR | Zbl