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The modified analytic trivialization of a family of real analytic mappings. (English) Zbl 0683.58007
Singularities, Proc. IMA Participating Inst. Conf., Iowa City/Iowa 1986, Contemp. Math. 90, 73-89 (1989).
[For the entire collection see Zbl 0668.00006.]
The author proves the following theorem. Theorem: Let \(f_ t(x):=F(x;t)\) be an analytic family of non-degenerate real analytic mappings. Suppose that the Newton polygons \(\Gamma_{f_ t}\) are independent of \(t\in I\). Let \(\pi\) : \(X\to {\mathbb{R}}^ n\) be one of the proper analytic modifications corresponding to the \(\Gamma_+(f_ t)\). Then the family F(x;t) admits an almost MAT via \(\pi\) along I. Moreover, if \(f_{t,\tau}\) is independent of t for each non-compact and non- coordinate face \(\tau\), then F admits a MAT via \(\pi\) along I. The author ends up with two examples that admit a MAT.
Reviewer: G.M.Rassias

58C05 Real-valued functions on manifolds