BI-LIPSCHITZ AND DIFFERENTIABLE SUFFICIENCY OF WEIGHTED JETS - Costa, João Carlos Ferreira [UNESP]; Saia, Marcelo José; Soares Junior, Carlos Humberto (Journal of Singularities, 2022)
In this work we study bi-Lipschitz and differential sufficiency in the set of weighted jets of map germs of weighted degree. Our main result improves the degree of sufficiency of jets in the classical jet space obtained by Takens and by Martins-Fávaro. Moreover, we give a condition for the bi-Lipschitz sufficiency in both the weighted and non-weighted cases. Bi-Lipschitz sufficiency was not considered in those previously cited works.
Keywords: sufficiency of jets; weighted jets