O Teorema de Poincaré-Bendixson para campos vetoriais contínuos na garrafa de Klein

Demuner, Daniela Paula

doi:10.11606/T.55.2009.tde-26022009-214414

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Doctoral Thesis

DOI

https://doi.org/10.11606/T.55.2009.tde-26022009-214414

Document

Doctoral Thesis

Author

Demuner, Daniela Paula (Catálogo USP)

Full name

Daniela Paula Demuner

E-mail

Institute/School/College

Instituto de Ciências Matemáticas e de Computação

Knowledge Area

Mathematics

Date of Defense

2009-02-05

Published

São Carlos, 2009

Supervisor

Federson, Márcia Cristina Anderson Braz (Catálogo USP)

Committee

Federson, Márcia Cristina Anderson Braz (President)
Apaza, Carlos Alberto Maquera
Cortez, Milton Edwin Cobo
Moreira, Carlos Gustavo Tamm de Araujo
Pires, Benito Frazão

Title in Portuguese

O Teorema de Poincaré-Bendixson para campos vetoriais contínuos na garrafa de Klein

Keywords in Portuguese

Campos vetoriais contínuos
Garrafa de Klein
Teorema de Poincaré-Bendixson
Trajetória fracamente recorrente
Trajetória recorrente

Abstract in Portuguese

Neste trabalho apresentamos uma versão do Teorema de Poincaré-Bendixson para campos vetoriais contínuos na garrafa de Klein. Como conseqüência, mostramos que a garrafa de Klein não possui campo vetorial contínuo com trajetória injetiva recorrente

Title in English

The Poincaré-Bendixson Theorem for continuous vector fields on the Klein bottle

Keywords in English

Continuous vector fields
Klein bottle
Poincaré-Bendixson Theorem
Recurrent trajectory
Weakly recurrent trajectory

Abstract in English

We present a version of the Poincaré-Bendixson Theorem on the Klein bottle for continuous vector fields. As a consequence, we obtain the fact that the Klein bottle does not admit continuous vector fields having a recurrent injective trajectory

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Publishing Date

2009-05-18

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