Author:
Nunes Pollyanna Vicente,Tal Fábio Armando
Abstract
Abstract
We study the relationship between transitivity and topological chaos for homeomorphisms of the two torus. We show that if a transitive homeomorphism of
T
2
is homotopic to the identity and has both a fixed point and a periodic point which is not fixed, then it has a topological horseshoe. We also show that if a transitive homeomorphisms of
T
2
is homotopic to a Dehn twist, then either it is aperiodic or it has a topological horseshoe.
Funder
Fundação de Amparo à Pesquisa do Estado de São Paulo
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics