Milnor fibrations on rho-tubes and rho-spheres for real analytic map germs

For a real analytic map germ $G:(\mathbb{R}^m,0)\to(\mathbb{R}^p,0)$, we study Milnor fibrations obtained by replacing the squared Euclidean distance with an analytic control function $ρ$ defining the origin. We formulate the corresponding Milnor set and condition (b), derive criteria for tube and s