Um estudo qualitativo do contraexemplo de Pinchuk

Detalhes bibliográficos
Autor(a) principal: Fernandes, Filipe Balduino Pires
Data de Publicação: 2017
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UFSCAR
Texto Completo: https://repositorio.ufscar.br/handle/ufscar/9544
Resumo: In this work we studied the topological behaviour of the level curves of the polinomial p of Pinchuk counterexample of the Real Jacobian Conjecture, namely, a polinomial non injective map of R^2 with the form (p,q) with a nonvanishing Jacobian Matrix determinant, using techniques of the qualitative theory of differential equations. We also found a family of polinomial functions witch are counterexamples of the Real Jacobian conjecture.
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spelling Fernandes, Filipe Balduino PiresBraun, Franciscohttp://lattes.cnpq.br/5890727692959507http://lattes.cnpq.br/0661563762546940a3bdc7cc-aa17-4908-9be6-c6a9b73de6402018-03-08T17:34:02Z2018-03-08T17:34:02Z2017-02-24FERNANDES, Filipe Balduino Pires. Um estudo qualitativo do contraexemplo de Pinchuk. 2017. Dissertação (Mestrado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2017. Disponível em: https://repositorio.ufscar.br/handle/ufscar/9544.https://repositorio.ufscar.br/handle/ufscar/9544In this work we studied the topological behaviour of the level curves of the polinomial p of Pinchuk counterexample of the Real Jacobian Conjecture, namely, a polinomial non injective map of R^2 with the form (p,q) with a nonvanishing Jacobian Matrix determinant, using techniques of the qualitative theory of differential equations. We also found a family of polinomial functions witch are counterexamples of the Real Jacobian conjecture.Neste trabalho estudamos o comportamento topológico das curvas de nível do polinômio p do contra-exemplo de Pinchuk à Conjectura Jacobiana Real, isto é, uma aplicação polinomial não injetora de R^2 da forma (p,q) com determinante da matriz Jacobiana que nunca se anula, utilizando técnicas da teoria qualitativa de equações diferenciais. Também encontramos uma família de aplicações polinomiais que são contraexemplos para a conjectura Jacobiana Real.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)porUniversidade Federal de São CarlosCâmpus São CarlosPrograma de Pós-Graduação em Matemática - PPGMUFSCarAnálise MatemáticaCampos vetoriaisInjetividadeMathematical analysisVector fieldsInjectivityCIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISEUm estudo qualitativo do contraexemplo de PinchukA qualitative study of the Pinchuk counterexampleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisOnline6006d79654d-81a9-44fe-b16c-b92d290c6f11info:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARLICENSElicense.txtlicense.txttext/plain; charset=utf-81957https://repositorio.ufscar.br/bitstream/ufscar/9544/3/license.txtae0398b6f8b235e40ad82cba6c50031dMD53ORIGINALFERNANDES_Filipe_2018.pdfFERNANDES_Filipe_2018.pdfapplication/pdf6418912https://repositorio.ufscar.br/bitstream/ufscar/9544/4/FERNANDES_Filipe_2018.pdf2092403246cfce55f420b119f20f98f4MD54TEXTFERNANDES_Filipe_2018.pdf.txtFERNANDES_Filipe_2018.pdf.txtExtracted texttext/plain148886https://repositorio.ufscar.br/bitstream/ufscar/9544/5/FERNANDES_Filipe_2018.pdf.txt88f934de4f318c04ac84e59f779bb9d7MD55THUMBNAILFERNANDES_Filipe_2018.pdf.jpgFERNANDES_Filipe_2018.pdf.jpgIM Thumbnailimage/jpeg6696https://repositorio.ufscar.br/bitstream/ufscar/9544/6/FERNANDES_Filipe_2018.pdf.jpgbe985aefb115007ee3c4ec03751f370fMD56ufscar/95442023-09-18 18:31:41.266oai:repositorio.ufscar.br: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Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:31:41Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false
dc.title.por.fl_str_mv Um estudo qualitativo do contraexemplo de Pinchuk
dc.title.alternative.eng.fl_str_mv A qualitative study of the Pinchuk counterexample
title Um estudo qualitativo do contraexemplo de Pinchuk
spellingShingle Um estudo qualitativo do contraexemplo de Pinchuk
Fernandes, Filipe Balduino Pires
Análise Matemática
Campos vetoriais
Injetividade
Mathematical analysis
Vector fields
Injectivity
CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE
title_short Um estudo qualitativo do contraexemplo de Pinchuk
title_full Um estudo qualitativo do contraexemplo de Pinchuk
title_fullStr Um estudo qualitativo do contraexemplo de Pinchuk
title_full_unstemmed Um estudo qualitativo do contraexemplo de Pinchuk
title_sort Um estudo qualitativo do contraexemplo de Pinchuk
author Fernandes, Filipe Balduino Pires
author_facet Fernandes, Filipe Balduino Pires
author_role author
dc.contributor.authorlattes.por.fl_str_mv http://lattes.cnpq.br/0661563762546940
dc.contributor.author.fl_str_mv Fernandes, Filipe Balduino Pires
dc.contributor.advisor1.fl_str_mv Braun, Francisco
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/5890727692959507
dc.contributor.authorID.fl_str_mv a3bdc7cc-aa17-4908-9be6-c6a9b73de640
contributor_str_mv Braun, Francisco
dc.subject.por.fl_str_mv Análise Matemática
Campos vetoriais
Injetividade
topic Análise Matemática
Campos vetoriais
Injetividade
Mathematical analysis
Vector fields
Injectivity
CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE
dc.subject.eng.fl_str_mv Mathematical analysis
Vector fields
Injectivity
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE
description In this work we studied the topological behaviour of the level curves of the polinomial p of Pinchuk counterexample of the Real Jacobian Conjecture, namely, a polinomial non injective map of R^2 with the form (p,q) with a nonvanishing Jacobian Matrix determinant, using techniques of the qualitative theory of differential equations. We also found a family of polinomial functions witch are counterexamples of the Real Jacobian conjecture.
publishDate 2017
dc.date.issued.fl_str_mv 2017-02-24
dc.date.accessioned.fl_str_mv 2018-03-08T17:34:02Z
dc.date.available.fl_str_mv 2018-03-08T17:34:02Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv FERNANDES, Filipe Balduino Pires. Um estudo qualitativo do contraexemplo de Pinchuk. 2017. Dissertação (Mestrado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2017. Disponível em: https://repositorio.ufscar.br/handle/ufscar/9544.
dc.identifier.uri.fl_str_mv https://repositorio.ufscar.br/handle/ufscar/9544
identifier_str_mv FERNANDES, Filipe Balduino Pires. Um estudo qualitativo do contraexemplo de Pinchuk. 2017. Dissertação (Mestrado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2017. Disponível em: https://repositorio.ufscar.br/handle/ufscar/9544.
url https://repositorio.ufscar.br/handle/ufscar/9544
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language por
dc.relation.confidence.fl_str_mv 600
dc.relation.authority.fl_str_mv 6d79654d-81a9-44fe-b16c-b92d290c6f11
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Universidade Federal de São Carlos
Câmpus São Carlos
dc.publisher.program.fl_str_mv Programa de Pós-Graduação em Matemática - PPGM
dc.publisher.initials.fl_str_mv UFSCar
publisher.none.fl_str_mv Universidade Federal de São Carlos
Câmpus São Carlos
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