• JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
 
  Bookmark and Share
 
 
Master's Dissertation
DOI
10.11606/D.55.2012.tde-13042012-101930
Document
Author
Full name
Leandro Antunes
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2012
Supervisor
Committee
Brandão, Daniel Smania (President)
Pires, Benito Frazão
Tahzibi, Ali
Title in Portuguese
Comportamento genérico de difeomorfismos do círculo
Keywords in Portuguese
Conjugação topológica
Difeomorfismo do círculo
Frações contínuas
Medida de Lebesqiue
Número de rotação
Abstract in Portuguese
Nós estudaremos o comportamento de difeomorfismos do círculo, tanto do ponto de vista combinatório quanto do ponto de vista topológico e da teoria da medida, seguindo os trabalhos de Michael Herman. A cada homeomorfismo do círculo podemos associar um número real positivo, denominado número de rotação. Mostraremos que existe um conjunto de números irracionais de medida de Lebesgue total na reta tal que, se f é um difeomorfismo do círculo de classe 'C POT. r ' que preserva a orientação, com r maior ou igual a 3 e com número de rotação nesse conjunto, então f é pelo menos 'C POT. r - 2' -conjugada a uma translação irracional. Além disso, mostraremos que dado um caminho 'f IND. t' de classe 'C POT. 1' definido em um intervalo [a;b] no conjunto dos difeomorfismos do círculo de classe 'C POT. r' que preservam a orientação, com r maior ou igual a 3, o conjunto dos parâmetros em que 'f IND. t' é 'C POT. r - 2' -conjugada a uma translação irracional tem medida de Lebesgue positiva, desde que os números de rotação em 'f IND. a' e 'f IND. b' sejam distintos
Title in English
Generic behavior of circle diffeomorphisms
Keywords in English
Circle diffeomorphisms
Continued fractions
Lebesgue measure
Rotation number
Topological conjugacy
Abstract in English
We will study the generic behavior of circle diffeomorphisms, in the combinatorial, topological and measure-theoretical sense, following the work of Michael Herman. To each order preserving homeomorphism of the circle we can associate a positive real number, called rotation number, which is invariant under conjugacy. We will show that there is a set of irrational numbers with full Lebesgue measure on R such that, if f is a circle diffeomorphism of class 'C POT. r', with r greater or equal 3 and with rotation number in that set, then f is at least 'C POT. r - 2' -conjugated to an irrational translation. Moreover, we will show that if ft is a 'C POT. 1' -path defined on a interval [a;b] over the set of the circle diffeomorphisms orientation preserving, with r '> or =' 3, then the set of parameters where 'f IND. t' is 'C POT. r - 2' -conjugated to a irrational translation has positive Lebesgue measure, since the rotation numbers of 'f IND. a' and 'f IND. b' are distinct
 
WARNING - Viewing this document is conditioned on your acceptance of the following terms of use:
This document is only for private use for research and teaching activities. Reproduction for commercial use is forbidden. This rights cover the whole data about this document as well as its contents. Any uses or copies of this document in whole or in part must include the author's name.
Publishing Date
2012-04-13
 
WARNING: Learn what derived works are clicking here.
All rights of the thesis/dissertation are from the authors
Centro de Informática de São Carlos
Digital Library of Theses and Dissertations of USP. Copyright © 2001-2021. All rights reserved.