Fukui, Toshizumi; Yoshinaga, Etsuo The modified analytic trivialization of family of real analytic functions. (English) Zbl 0559.58005 Invent. Math. 82, 467-477 (1985). 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. Cited in 1 ReviewCited in 13 Documents MSC: 58C05 Real-valued functions on manifolds Keywords:modified analytic trivialization; real analytic functions; Newton principal part Citations:Zbl 0509.58007 PDFBibTeX XMLCite \textit{T. Fukui} and \textit{E. Yoshinaga}, Invent. Math. 82, 467--477 (1985; Zbl 0559.58005) Full Text: DOI EuDML 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 [4] Kuo, T.C., Ward, J.N.: A theorem on almost analytic equisingularity. J. Math. Soc. Japan33, 471-484 (1981) · Zbl 0476.58004 [5] Varchenko, A.N.: Newton polyhedra and estimation of oscillating integrals. Funct. Anal. Appl.10, 175-196 (1977) · Zbl 0351.32011 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.