Bi-Lipschitz A-triviality of map germs and Newton filtrations

This article is devoted to criteria of Lipschitz equisingularity for families of real analytic map germs from (Rn,0) to (Rp,0) with n⩾p like gλ(x)=g(x)+λh(x), where λ is a small real number. The main result of this article, Theorem 4.2 states a condition on the order of the terms of h(x), in such a way that the family gλ is bi-Lipschitz A-trivial. Theorem 4.2 gives the conditions in terms of Newton polyhedron associated to the germ g. The tools used here are based in the construction of convenient controlled vector fields.