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Equivalence of differentiable functions, rational functions and polynomials

Masahito Shiota (1982)

Annales de l'institut Fourier

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.

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