Trabalho apresentado em evento
Bi-Lipschitz G-triviality and Newton polyhedra, G = R, C, K, R-V, C-V, K-V
Fecha
2012-01-01Registro en:
Real and Complex Singularities. Providence: Amer Mathematical Soc, v. 569, p. 29-43, 2012.
0271-4132
10.1090/conm/569/11248
WOS:000308439300003
Autor
Universidade Estadual Paulista (Unesp)
Resumen
In this work we provide estimates for the bi-Lipschitz G-triviality, G = C or K, for a family of map germs satisfying a Lojasiewicz condition. We work with two cases: the class of weighted homogeneous map germs and the class of non-degenerate map germs with respect to some Newton polyhedron. We also consider the bi-Lipschitz triviality for families of map germs defined on an analytic variety V. We give estimates for the bi-Lipschitz G(V)-triviality where G = R,C or K in the weighted homogeneous case. Here we assume that the map germ and the analytic variety are both weighted homogeneous with respect to the same weights. The method applied in this paper is based in the construction of controlled vector fields in the presence of a suitable Lojasiewicz condition. In the last section of this work we compare our results with other results related to this work showing tables with all estimates that we know, including ours.