Lightly chaotic functional envelopes
Dynamical Systems
2021-12-23 v1 General Topology
Abstract
In this paper we introduce some weak dynamical properties by using subbases for the phase space. Among them, the notion of light chaos is the most significant. Severalexamples, which clarify the relationships between this kind of chaos and some classical notions, are given. Particular attention is also devoted to the connections between the dynamical properties of a system and the dynamical properties of the associated functional envelope. We show, among other things, that a continuous map f : X ! X, where X is a metric space, is chaotic (in the sense of Devaney) if and only if the associated functional dynamical system is lightly chaotic.
Cite
@article{arxiv.2112.11780,
title = {Lightly chaotic functional envelopes},
author = {Annamaria Miranda},
journal= {arXiv preprint arXiv:2112.11780},
year = {2021}
}
Comments
18 pages, submitted