Smooth pertubations of Lorenz-like flows

Vidarte, José Humberto Bravo

doi:10.11606/T.55.2014.tde-15072014-155326

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Doctoral Thesis

DOI

https://doi.org/10.11606/T.55.2014.tde-15072014-155326

Document

Doctoral Thesis

Author

Vidarte, José Humberto Bravo (Catálogo USP)

Full name

José Humberto Bravo Vidarte

E-mail

Institute/School/College

Instituto de Ciências Matemáticas e de Computação

Knowledge Area

Mathematics

Date of Defense

2014-04-04

Published

São Carlos, 2014

Supervisor

Brandão, Daniel Smania (Catálogo USP)

Committee

Brandão, Daniel Smania (President)
Araújo, Vítor Domingos Martins de
Mendoza, Alexander Eduardo Arbieto
Pacífico, Maria José

Title in English

Smooth pertubations of Lorenz-like flows

Keywords in English

Foliations
Lorenz like flows
Lorenz-type maps

Abstract in English

Given a Geometric Lorenz Flow X on 'R POT. n+2' of class 'C POT. k+1'; by definition there exists a Poincaré map 'P IND. X' of class 'C POT. k+1'; often so-called Lorenz-type map [ABS83]. The main purpose in this dissertation is to show that under certain conditions the Lorenz-type map 'P IND.X' can be associate to it a one-dimensional transformation 'f IND. X' of class 'C POT. k' (defined on an interval). This association is so-called the reduction transformation R; so we have 'RP IND. X' = 'f IND. X'. This association would allow us to study the dynamical properties for the original flow using techniques of one-dimensional dynamics of class 'C POT. k'

Title in Portuguese

Pertubações suaves de aplicações tipo Lorenz

Keywords in Portuguese

Aplicações tipo Lorenz
Fluxos tipo Lorenz

Abstract in Portuguese

Dado um Fluxo Geométrico de Lorenz X em 'R POT. n+2' de classe 'C POT. k+1'; por definição, existe uma aplicação de Poincaré 'P IND. X'' de classe 'C POT. k+1'; frequentemente chamado aplicação do tipo Lorenz [ABS83]. O objetivo principal desta tese é mostrar que, sob certas condições a aplicação do tipo Lorenz 'P IND. X' pode ser associado a ele uma transformação unidimensional 'f IND. X' de classe 'C POT. k' (definida em um intervalo). Esta associação é chamada de transformação de redução R; assim temos que , 'RP IND. X' = 'f IND. X'. Esta associação nos permitiria estudar as propriedades dinâmicas do fluxo original utilizando técnicas da dinâmica unidimensional de classe 'C POT. k'

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Publishing Date

2014-07-15

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