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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

$ \mathcal{K}$-bi-Lipschitz equivalence of real function-germs


Authors: L. Birbrair, J. C. F. Costa, A. Fernandes and M. A. S. Ruas
Journal: Proc. Amer. Math. Soc. 135 (2007), 1089-1095
MSC (2000): Primary 32S15, 32S05
Published electronically: October 27, 2006
MathSciNet review: 2262910
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Abstract: In this paper we prove that the set of equivalence classes of germs of real polynomials of degree less than or equal to $ k$, with respect to $ \mathcal{K}$-bi-Lipschitz equivalence, is finite.


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Additional Information

L. Birbrair
Affiliation: Departamento de Matemàtica, Universidade Federal do Cearà, Av. Mister Hull s/u Campus do PICI, Bloco 914, CEP 60, 455-760 Fortaleza-CE, Brazil

J. C. F. Costa
Affiliation: Departamento de Matemàtica (IBILCE), Universidade Estadual Paulista, Sao Jose de Rio Preto, SP 15054-000 Brazil

A. Fernandes
Affiliation: Departamento de Matemàtica, Universidade Federal do Cearà, Av. Mister Hull s/u Campus do PICI, Bloco 914, CEP 60, 455-760 Fortaleza-CE, Brazil

M. A. S. Ruas
Affiliation: Institute of Sciences and Mathematics, University of Sao Paulo, Sao Carlos SP, Brazil

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08566-2
PII: S 0002-9939(06)08566-2
Received by editor(s): May 14, 2005
Received by editor(s) in revised form: November 4, 2005
Published electronically: October 27, 2006
Additional Notes: The first named author was supported by CNPq grant No. 300985/93-2.
The second named author was supported by Fapesp grant No. 01/14577-0.
The fourth named author was supported by CNPq grant No. 301474/2005-2.
Communicated by: Mikhail Shubin
Article copyright: © Copyright 2006 American Mathematical Society