Geodesic
Chaos and Shadowing in General Systems
Kragujevac Journal of Mathematics, Tome 46 (2022) no. 3, p. 383

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

In this paper we describe some basic notions of topological dynamical systems for maps of type $f:X×X\rightarrow X$ named general systems. This is proved that every uniformly expansive general system has the shadowing property and every uniformly contractive general system has the (asymptotic) average shadowing and shadowing properties. In the rest, Devaney chaos for general systems is considered. Also, we show that topological transitivity and density of periodic points of a general systems imply topological ergodicity. We also obtain some results on the topological mixing and sensitivity for general systems.
Classification : 37B50, 37C15
Keywords: chaos, general system, shadowing, transitive 
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     title = {Chaos and {Shadowing} in {General} {Systems}},
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M. Fatehi Nia; A. Zamani Bahabadi. Chaos and Shadowing in General Systems. Kragujevac Journal of Mathematics, Tome 46 (2022) no. 3, p. 383 . http://geodesic.mathdoc.fr/item/KJM_2022_46_3_a3/