Flows with ergodic pseudo orbit tracing property

Autor:	Manseob Lee
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	pseudo orbit tracing property ergodic pseudo orbit tracing property chain transitive transitive star condition hyperbolic Mathematics QA1-939 Applied mathematics. Quantitative methods T57-57.97
Zdroj:	Electronic Research Archive, Vol 30, Iss 7, Pp 2406-2416 (2022)
Druh dokumentu:	article
ISSN:	2688-1594
DOI:	10.3934/era.2022122?viewType=HTML
Popis:	In the manuscript, we deal with a type of pseudo orbit tracing property and hyperbolicity about a vector field (or a divergence free vector field). We prove that a vector field (or a divergence free vector field) of a smooth closed manifold $ M $ has the robustly ergodic pseudo orbit tracing property then it does not contain any singularities and it is Anosov. Additionally, there is a dense and open set $ \mathcal{R} $ in the set of $ C^1 $ a vector field (or a divergence free vector field) of a smooth closed manifold $ M $ such that given a vector field (or a divergence free vector field) has the ergodic pseudo orbit tracing property then it does not contain singularities and it is Anosov.
Databáze:	Directory of Open Access Journals
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