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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

##### MSC:
 58C05 Real-valued functions on manifolds