On the periodic orbits, shadowing and strong transitivity of continuous flows. (October 2018)

• Record Type: Journal Article
• Authors: Bessa, Mário; Torres, Maria Joana; Varandas, Paulo
• Is Part Of: Nonlinear analysis. Volume 175(2018)
• Page Start: 191
• Page End: 209
• Publication Date: 2018-10
• Subjects: primary 53D25 37B20 -- secondary 37C50; Gluing orbit property -- Shadowing -- Periodic orbits; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.06.002
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove that chaotic flows (i.e. flows that satisfy the shadowing property and have a dense subset of periodic orbits) satisfy a reparametrized gluing orbit property similar to the one introduced in Bomfim and Varandas (2015). In particular, these are strongly transitive in balls of uniform radius. We also prove that the shadowing property for a flow and a generic time- t map, and having a dense subset of periodic orbits hold for a C 0 -Baire generic subset of Lipschitz vector fields, that generate continuous flows. Similar results also hold for C 0 -generic homeomorphisms and, in particular, we deduce that chain recurrent classes of C 0 -generic homeomorphisms have the gluing orbit property.