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    Costa, J. C. F. Nishimura, T. and Ruas, M. A. S. 2014. Bi-Lipschitz $$\mathcal A $$ -equivalence of $$\mathcal K $$ -equivalent map-germs. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, Vol. 108, Issue. 1, p. 173.


    Costa, João Carlos Ferreira Saia, Marcelo José and Soares Junior, Carlos Humberto 2012. Bi-Lipschitz <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi mathvariant="script">A</mml:mi></mml:math>-triviality of map germs and Newton filtrations. Topology and its Applications, Vol. 159, Issue. 2, p. 430.


    Ruas, Maria Aparecida Soares and Valette, Guillaume 2011. C 0 and bi-Lipschitz $${\mathcal{K}}$$ -equivalence of mappings. Mathematische Zeitschrift, Vol. 269, Issue. 1-2, p. 293.


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Existence of Moduli for Bi-Lipschitz Equivalence of Analytic Functions

  • Jean-Pierre Henry (a1) and Adam Parusiński (a2)
  • DOI: http://dx.doi.org/10.1023/A:1022726806349
  • Published online: 01 April 2003
Abstract

We show that the bi-Lipschitz equivalence of analytic function germs (${\open C}^{2}$, 0)→(${\open C}$, 0) admits continuous moduli. More precisely, we propose an invariant of the bi-Lipschitz equivalence of such germs that varies continuously in many analytic families ft: (${\open C}^{2}$, 0)→(${\open C}$, 0). For a single germ f the invariant of f is given in terms of the leading coefficients of the asymptotic expansions of f along the branches of generic polar curve of f.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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