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

Abstract

This article is devoted to criteria of Lipschitz equisingularity for families of real analytic map germs from (R-n. 0) to (R-p.0) with n >= p like g(lambda)(x) = g(x) + lambda h(x), where lambda 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 g(lambda) 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. (C) 2011 Elsevier B.V. All rights reserved.