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Topological horseshoes for transitive 2-torus homeomorphisms

Nunes, Pollyanna Vicente

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Título:
Topological horseshoes for transitive 2-torus homeomorphisms
Autor: Nunes, Pollyanna Vicente
Orientador: Tal, Fabio Armando
Assuntos: Dehn Twist; Ferradura Topológica; Homeomorfismo; Toro; Isotópico À Identidade; Dehn Twist; Topological Horseshoe; Isotopic To Identity; Homeomorphism; Torus
Notas: Tese (Doutorado)
Descrição: Based on rotation theory and forcing theory for transverse trajectories of surface homeomorphisms, in this work we study the relation between transitive homeomorphism of the 2-torus and the existence of a topological horseshoe. Let f be a transitive homeomorphism of the 2-torus. In the case where f is isotopic to the identity, we show that f has a topological horseshoe, if f has a fixed point and a non-fixed periodic point. In the case where a power f^k, k > 1, is isotopic to identity but f itself is not, we show that if f has at least one fixed point and has no topological horseshoe then the rotation set of some lift of f to the plane is only the origin. We also study the case where a power f^k, k 1, of f is isotopic to Dehn twist. In this case we show that f has a topological horseshoe, if f has at least a fixed point.
DOI: 10.11606/T.45.2021.tde-30062021-104510
Editor: Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Instituto de Matemática e Estatística
Data de criação/publicação: 2021-06-11
Formato: Adobe PDF
Idioma: Inglês

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