Multi--Lipschitz equivalence in dimension two
arXiv:2304.06610
Abstract
In this paper, we study Multi--equivalence of multi-germs of functions on the plane, definable in a polynomially bounded o-minimal structure. We partition the germ of the plane at origin into zones of arcs in such a way that it produces a non-Archimedean space (set of orders and width functions) compatible with a given multigerm, encoding its asymptotic behaviour. Such a partition is called Multipizza. We show the existence, uniqueness and complete invariance of Multipizzas with respect to the Multi--Lipschitz equivalence.
11 pages