Bi-Lipschitz G-triviality and Newton polyhedra, G = R, C, K, R-V, C-V, K-V
Autor(a) principal: | |
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Data de Publicação: | 2012 |
Outros Autores: | , |
Tipo de documento: | Artigo de conferência |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1090/conm/569/11248 http://hdl.handle.net/11449/22147 |
Resumo: | In this work we provide estimates for the bi-Lipschitz G-triviality, G = C or K, for a family of map germs satisfying a Lojasiewicz condition. We work with two cases: the class of weighted homogeneous map germs and the class of non-degenerate map germs with respect to some Newton polyhedron. We also consider the bi-Lipschitz triviality for families of map germs defined on an analytic variety V. We give estimates for the bi-Lipschitz G(V)-triviality where G = R,C or K in the weighted homogeneous case. Here we assume that the map germ and the analytic variety are both weighted homogeneous with respect to the same weights. The method applied in this paper is based in the construction of controlled vector fields in the presence of a suitable Lojasiewicz condition. In the last section of this work we compare our results with other results related to this work showing tables with all estimates that we know, including ours. |
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Bi-Lipschitz G-triviality and Newton polyhedra, G = R, C, K, R-V, C-V, K-Vbi-Lipschitz determinacyNewton filtrationcontrolled vector fieldsIn this work we provide estimates for the bi-Lipschitz G-triviality, G = C or K, for a family of map germs satisfying a Lojasiewicz condition. We work with two cases: the class of weighted homogeneous map germs and the class of non-degenerate map germs with respect to some Newton polyhedron. We also consider the bi-Lipschitz triviality for families of map germs defined on an analytic variety V. We give estimates for the bi-Lipschitz G(V)-triviality where G = R,C or K in the weighted homogeneous case. Here we assume that the map germ and the analytic variety are both weighted homogeneous with respect to the same weights. The method applied in this paper is based in the construction of controlled vector fields in the presence of a suitable Lojasiewicz condition. In the last section of this work we compare our results with other results related to this work showing tables with all estimates that we know, including ours.UNESP, IBILCE, Dept Matemat, Sao Jose do Rio Preto, SP, BrazilUNESP, IBILCE, Dept Matemat, Sao Jose do Rio Preto, SP, BrazilAmer Mathematical SocUniversidade Estadual Paulista (Unesp)Costa, J. C. F. [UNESP]Saia, M. J.Soares Junior, C. H.2014-05-20T14:02:52Z2014-05-20T14:02:52Z2012-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObject29-43http://dx.doi.org/10.1090/conm/569/11248Real and Complex Singularities. Providence: Amer Mathematical Soc, v. 569, p. 29-43, 2012.0271-4132http://hdl.handle.net/11449/2214710.1090/conm/569/11248WOS:000308439300003Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengReal and Complex Singularitiesinfo:eu-repo/semantics/openAccess2021-10-23T21:41:22Zoai:repositorio.unesp.br:11449/22147Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462021-10-23T21:41:22Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Bi-Lipschitz G-triviality and Newton polyhedra, G = R, C, K, R-V, C-V, K-V |
title |
Bi-Lipschitz G-triviality and Newton polyhedra, G = R, C, K, R-V, C-V, K-V |
spellingShingle |
Bi-Lipschitz G-triviality and Newton polyhedra, G = R, C, K, R-V, C-V, K-V Costa, J. C. F. [UNESP] bi-Lipschitz determinacy Newton filtration controlled vector fields |
title_short |
Bi-Lipschitz G-triviality and Newton polyhedra, G = R, C, K, R-V, C-V, K-V |
title_full |
Bi-Lipschitz G-triviality and Newton polyhedra, G = R, C, K, R-V, C-V, K-V |
title_fullStr |
Bi-Lipschitz G-triviality and Newton polyhedra, G = R, C, K, R-V, C-V, K-V |
title_full_unstemmed |
Bi-Lipschitz G-triviality and Newton polyhedra, G = R, C, K, R-V, C-V, K-V |
title_sort |
Bi-Lipschitz G-triviality and Newton polyhedra, G = R, C, K, R-V, C-V, K-V |
author |
Costa, J. C. F. [UNESP] |
author_facet |
Costa, J. C. F. [UNESP] Saia, M. J. Soares Junior, C. H. |
author_role |
author |
author2 |
Saia, M. J. Soares Junior, C. H. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Costa, J. C. F. [UNESP] Saia, M. J. Soares Junior, C. H. |
dc.subject.por.fl_str_mv |
bi-Lipschitz determinacy Newton filtration controlled vector fields |
topic |
bi-Lipschitz determinacy Newton filtration controlled vector fields |
description |
In this work we provide estimates for the bi-Lipschitz G-triviality, G = C or K, for a family of map germs satisfying a Lojasiewicz condition. We work with two cases: the class of weighted homogeneous map germs and the class of non-degenerate map germs with respect to some Newton polyhedron. We also consider the bi-Lipschitz triviality for families of map germs defined on an analytic variety V. We give estimates for the bi-Lipschitz G(V)-triviality where G = R,C or K in the weighted homogeneous case. Here we assume that the map germ and the analytic variety are both weighted homogeneous with respect to the same weights. The method applied in this paper is based in the construction of controlled vector fields in the presence of a suitable Lojasiewicz condition. In the last section of this work we compare our results with other results related to this work showing tables with all estimates that we know, including ours. |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012-01-01 2014-05-20T14:02:52Z 2014-05-20T14:02:52Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/conferenceObject |
format |
conferenceObject |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1090/conm/569/11248 Real and Complex Singularities. Providence: Amer Mathematical Soc, v. 569, p. 29-43, 2012. 0271-4132 http://hdl.handle.net/11449/22147 10.1090/conm/569/11248 WOS:000308439300003 |
url |
http://dx.doi.org/10.1090/conm/569/11248 http://hdl.handle.net/11449/22147 |
identifier_str_mv |
Real and Complex Singularities. Providence: Amer Mathematical Soc, v. 569, p. 29-43, 2012. 0271-4132 10.1090/conm/569/11248 WOS:000308439300003 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Real and Complex Singularities |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
29-43 |
dc.publisher.none.fl_str_mv |
Amer Mathematical Soc |
publisher.none.fl_str_mv |
Amer Mathematical Soc |
dc.source.none.fl_str_mv |
Web of Science reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1799964417740242944 |