On the periodic orbits, shadowing and strong transitivity of continuous flows. (October 2018) - Bessa, Mário; Torres, Maria Joana; Varandas, Paulo
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.