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TitleTopological aspects of incompressible flows
Author(s)Bessa, Mário
Torres, M. J.
Varandas, Paulo
KeywordsPeriodic points
Topological dynamics
Periodic shadowing
Closing lemma
Gluing orbit property
Issue date2021
JournalJournal of Differential Equations
Abstract(s)In this article we approach some of the basic questions in topological dynamics, concerning periodic points, transitivity, the shadowing and the gluing orbit properties, in the context of C0-incompressible flows generated by Lipschitz vector fields. We prove that a C0-generic incompressible and fixed-point free flow satisfies the periodic shadowing property, it is transitive and has a dense set of periodic points in the non-wandering set. In particular, a C0-generic fixed-point free incompressible flow satisfies the reparametrized gluing orbit property. We also prove that C0-generic incompressible flows satisfy the general density theorem and the weak shadowing property, moreover these are transitive.
Publisher version
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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