On definition of Devaney chaos for a continuous group action on a Hausdorff uniform space

Autor:	Volna, Barbora
Rok vydání:	2020
Předmět:	Mathematics - Dynamical Systems Mathematics - General Topology 37B05 54H11 37D45 34A60
Druh dokumentu:	Working Paper
Popis:	We show that the existence of a dense set of periodic points for a topologically transitive non-minimal continuous group action on a Hausdorff uniform space with an infinite acting group does not necessarily imply a sensitive dependence to the initial conditions in such a system. This leads to define the chaos in the sense of Devaney for a continuous group action on a Hausdorff uniform spaces with an infinite acting group in the original way, i.e. a non-minimal topologically transitive and sensitive system with a dense set of periodic points is a chaotic system in the sense of Devaney. Comment: 10 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2011.13975 Zobrazit plný text záznamu View this record from Arxiv