Publication
On the periodic orbits, shadowing and strong transitivity of continuous flows
| Summary: | 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. |
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| Main Authors: | Bessa, Mário |
| Other Authors: | Torres, M. J.; Varandas, Paulo |
| Subject: | Gluing orbit property Shadowing Periodic orbits Ciências Naturais::Matemáticas |
| Year: | 2018 |
| Country: | Portugal |
| Document type: | article |
| Access type: | restricted access |
| Associated institution: | Universidade do Minho |
| Language: | English |
| Origin: | RepositóriUM - Universidade do Minho |
| Summary: | 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. |
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