Fibration theorems à la Milnor for analytic maps with non-isolated singularities

We study the topology of real analytic maps in a neighborhood of a (possibly non-isolated) critical point. We prove fibration theorems à la Milnor for real analytic maps with non-isolated critical values. Here we study the situation for maps with arbitrary critical set. We use the concept of d-regularity introduced in an earlier paper for maps with an isolated critical value. We prove that this is the key point for the existence of a Milnor fibration on the sphere in the general setting. Plenty of examples are discussed along the text, particularly the interesting family of functions (f, g) : Rn→ R2 of the type (f,g)=(∑i=1naixip,∑i=1nbixiq), where ai, bi∈ R are constants in generic position and p, q≥ 2 are integers.