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Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2017.tde-14122017-114529
Document
Author
Full name
Daniela Paula Demuner
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2005
Supervisor
Committee
Vidalon, Carlos Teobaldo Gutierrez (President)
Tahzibi, Ali
Teixeira, Marco Antonio
 
Title in Portuguese
Resultados recentes relativos à conjectura fraca de Markus-Yamabe
Keywords in Portuguese
Não disponível
Abstract in Portuguese
C. Olech |28] provou que os problemas de estabilidade assintótica global de campos de vetores no Rn e injetividade global de aplicações do Rn nele próprio estão interrelacionados. Neste contexto, deparamo-nos com a Conjectura Fraca de Markus-Yamabe, cujo enunciado é o seguinte: Se F : Rn → Rn é uma aplicação de classe Cl tal que para todo ponto p ∈ Rn, todos os autovalores da derivada DF(p) têm parte real negativa, então F é uma aplicação injetiva. O objetivo deste trabalho é apresentar alguns resultados referentes a esta conjectura.
 
Title in English
Not available
Keywords in English
Not available
Abstract in English
It has been shown by C. Olech [28] that global asymptotic stability of vector fields of Rn and global injectivity of maps from Rn into itself are interrelated problems. In this context we have the Weak Markus-Yamabe Conjecture whose statement is as follows: If F : Rn → Rn be a C1 map such that for all p ∈ Rn, all the eigenvalues of the derivative DF(p) have negativo real part, then F is an injective map. In this work we present, some results related to this conjecture.
 
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Publishing Date
2017-12-14
 
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