Equivalence of differentiable functions, rational functions and polynomials
Annales de l'Institut Fourier, Volume 32 (1982) no. 4, p. 167-204

We show under some assumptions that a differentiable function can be transformed globally to a polynomial or a rational function by some diffeomorphism. One of the assumptions is that the function is proper, the number of critical points is finite, and the Milnor number of the germ at each critical point is finite.

Nous montrons sous certaines hypothèses qu’une fonction différentiable peut être transformée globablement en un polynôme ou une fonction rationnelle par un difféomorphisme. Une des hypothèses est que la fonction est propre, le nombre des points critiques est fini, et le nombre de Milnor du germe en chaque point critique est fini.

@article{AIF_1982__32_4_167_0,
     author = {Shiota, Masahito},
     title = {Equivalence of differentiable functions, rational functions and polynomials},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {32},
     number = {4},
     year = {1982},
     pages = {167-204},
     doi = {10.5802/aif.899},
     zbl = {0466.58006},
     mrnumber = {84i:58023},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1982__32_4_167_0}
}
Shiota, Masahito. Equivalence of differentiable functions, rational functions and polynomials. Annales de l'Institut Fourier, Volume 32 (1982) no. 4, pp. 167-204. doi : 10.5802/aif.899. http://www.numdam.org/item/AIF_1982__32_4_167_0/

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