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The modified analytic trivialization of family of real analytic functions. (English) Zbl 0559.58005
In [J. Math. Soc. Japan 32, 605-614 (1980; Zbl 0509.58007)], T.-C. Kuo introduced the notion of modified analytic trivialization (MAT) in a family of real analytic functions. This notion induces an equivalence relation in the set of all germs of real analytic functions, which is slightly weaker than bianalyticity and much stronger than homeomorphism. In this note we give a criterion of MAT. For example, for non-degenerate and convenient functions, the MAT type is determined by the Newton principal part.

MSC:
58C05 Real-valued functions on manifolds
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References:
[1] Kaneko, A.: Newton polygon, singularities and oscillating integrals. Math. Lect. Note Sophia Univ.11 (1981) (Japanese) · Zbl 0549.58010
[2] Kempf, G., Knudsen, F., Mumford, D., Saint-Donat, B.: Toroidal Embeddings, I. Lect. Notes Math., vol. 339. Berlin, Heidelberg, New York: Springer 1973 · Zbl 0271.14017
[3] Kuo, T.C.: The modified analytic trivialization of singularities. J. Math. Soc. Japan32, 605-614 (1980) · Zbl 0509.58007 · doi:10.2969/jmsj/03240605
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