We consider various notions from the theory of dynamical systems from a topological point of
view. Many of these notions can be sensibly defined either in terms of (finite) open covers or …

Shifts of finite type and the notion of shadowing, or pseudo-orbit tracing, are powerful tools in
the study of dynamical systems. In this paper we prove that there is a deep and fundamental …

We discuss the notions of positive expansivity, chain transitivity, uniform rigidity, chain
mixing, weak specification, and pseudo orbital specification in terms of finite open covers for …

In this paper, two topological versions of quasi-shadowing property defined in terms of finite
open covers and uniformities are introduced, which coincide on compact Hausdorff spaces …

Let $\sigma $ denote the shift automorphism on $\mathcal {P}(\omega)/\mathrm {fin} $,
defined by setting $\sigma ([A])=[A+ 1] $ for all $ A\subseteq\omega $. We show that the …

We define the notions of ergodic shadowing property, ḏ-shadowing property and eventual
shadowing property in terms of the topology of the phase space. Secondly we define these …

The shift map, denoted σ, is the self-homeomorphism of Image 1 induced by the successor
function n↦ n+ 1 on ω. We prove that the isomorphism classes of σ and σ− 1 cannot be …

We consider the notions of equicontinuity point, sensitivity point and so on from a topological
point of view. Many of these notions can be sensibly defined either in terms of (finite) open …

Does P()Fin know its right hand from its left? Part 3 Page 1 Does P(ω)/Fin know its right hand
from its left? Part 3 Will Brian January 27, 2025 University of North Carolina at Charlotte Page …

We prove that for every countable discrete group G, there is a G-flow on ω* that has every G-
flow of weight≤ ℵ 1 as a quotient. It follows that, under the Continuum Hypothesis, there is a …