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

Bessa, Mário; Torres, Maria Joana; Varandas, Paulo

http://hdl.handle.net/10400.2/13864

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Authors

Bessa, Mário

Torres, Maria Joana

Varandas, Paulo

Abstract(s)

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 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.

Keywords

Gluing orbit property Shadowing Periodic orbits

URI

http://hdl.handle.net/10400.2/13864

Citation

M. Bessa, M. J. Torres, P. Varandas, On the periodic orbits, shadowing and strong transitivity of continuous flows,Nonlinear Analysis, 175, 191-209, 2018