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Doctoral Thesis
DOI
Document
Author
Full name
Guilherme Silva Salomão
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2019
Supervisor
Committee
Tal, Fabio Armando (President)
Kocsard, Alejandro
Koropecki, Andrés
Robles, Alejandro Miguel Passeggi Diaz
Zanata, Salvador Addas
Title in Portuguese
Inexistência de difusão sublinear para uma classe de homeomorfismos do toro
Keywords in Portuguese
Conjunto de rotação
Difusão sublinear
Dinâmica topológica
Homeomorfismos do toro
Abstract in Portuguese
No presente trabalho iremos provar, usando a folheação de Brouwer-Le Calvez e a teoria de forcing dela derivada, que dado um homeomorfismo f do toro isotópico à identidade tal que seu conjunto de rotação é um segmento de reta com inclinação irracional e tendo 0 como um ponto extremal, então f não possui difusão sublinear na direção perpendicular à direção do conjunto de rotação
Title in English
Inexistence of sublinear diffusion for a class of torus homeomorphisms
Keywords in English
Rotation set
Sublinear diffusion
Topological dynamics
Torus homeomorphisms
Abstract in English
In the present work we will prove, using the Brouwer-Le Calvez foliation and the forcing theory derived from it, that given a torus homeomorphism f isotopopic to the identity such that its rotation set is a line segment with irrational slope and 0 is an extreme point, then f does not have sublinear diffusion in the direction perpendicular to the direction of the rotation set.
 
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Publishing Date
2019-07-04
 
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