Infinitesimal bi-Lipschitz Equivalence of Functions

Abstract: We introduce two different notions of infinitesimal bi-Lipschitz equivalence for functions, one related to bi-Lipschitz triviality of families of functions, one related to homeomorphisms which are bi-Lipschitz on the fibers of the functions in the family. We show that the first is not a generic condition, and that the second is.