caa a22 4500 445836849 CHVBK 20180317145332.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00209-010-0728-z doi (NATIONALLICENCE)springer-10.1007/s00209-010-0728-z C 0 and bi-Lipschitz $${\mathcal{K}}$$ -equivalence of mappings [Elektronische Daten] [Maria Ruas, Guillaume Valette] In this paper we investigate the classification of mappings up to $${\mathcal{K}}$$-equivalence. We give several results of this type. We study semialgebraic deformations up to semialgebraic C 0 $${\mathcal{K}}$$-equivalence and bi-Lipschitz $${\mathcal{K}}$$-equivalence. We give an algebraic criterion for bi-Lipschitz $${\mathcal{K}}$$-triviality in terms of semi-integral closure (Theorem 3.5). We also give a new proof of a result of Nishimura: we show that two germs of smooth mappings $${f, g: \mathbb{R}^n \to \mathbb{R}^n}$$, finitely determined with respect to $${\mathcal{K}}$$-equivalence are C 0-$${\mathcal{K}}$$-equivalent if and only if they have the same degree in absolute value. The Author(s), 2010 Ruas Maria Departamento de Matemática, Instituto de Ciências, Matemáticas e de Computação, Universidade de São Paulo, Campus de São Carlos, Caixa Postal 668, 13560-970, São Carlos, SP, Brazil aut Valette Guillaume Instytut Matematyczny PAN, ul. Św. Tomasza 30, 31-027, Kraków, Poland aut Mathematische Zeitschrift Springer-Verlag 269/1-2(2011-10-01), 293-308 0025-5874 269:1-2<293 2011 269 209 https://doi.org/10.1007/s00209-010-0728-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0728-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ruas Maria Departamento de Matemática, Instituto de Ciências, Matemáticas e de Computação, Universidade de São Paulo, Campus de São Carlos, Caixa Postal 668, 13560-970, São Carlos, SP, Brazil aut NATIONALLICENCE 700 1- Valette Guillaume Instytut Matematyczny PAN, ul. Św. Tomasza 30, 31-027, Kraków, Poland aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 269/1-2(2011-10-01), 293-308 0025-5874 269:1-2<293 2011 269 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer