Uniform (m)-condition and Strong Milnor fibrations

Abstract

In this paper we study the Milnor fibrations associated to real analytic map germs $\psi :({\mathbb{R}}^m,0)\to ({\mathbb{R}}^2,0)$ with isolated critical point at $0\in {\mathbb{R}}^m$. The main result relates the existence of called Strong Milnor fibrations with a transversality condition of a convenient family of analytic varieties with isolated critical points at the origin $0\in {\mathbb{R}}^m$, obtained by projecting the map germ $\psi$ in the family $L_{-\theta }$ of all lines through the origin in the plane ${\mathbb{R}}^2.$