On the periodic orbits, shadowing and strong transitivity of continuous flows

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 [7]. 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 C0-Baire generic subset of Lipschitz vector fields, that generate continuous flows. Similar results also hold for C0-generic homeomorphisms and, in particular, we deduce that chain recurrent classes of C0-generic homeomorphisms have the gluing orbit property.
The authors would like also to thank the reviewer for his/her careful reading of the manuscript and the helpful comments. MB was partially supported by FCT - ‘Funda¸c˜ao para a Ciˆencia e a Tecnologia’, through CMA-UBI, project UID/MAT/00212/2013. He would also like to thank CMUP for providing the necessary conditions in which this work was developed. MJT was partially supported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the ‘Funda¸c˜ao para a Ciˆencia e a Tecnologia’, through the Project UID/MAT/00013/2013. PV was partially supported by BREUDS and CNPq-Brazil.
info:eu-repo/semantics/publishedVersion