Joseph Auslander
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View article: Some relations in topological dynamics
Some relations in topological dynamics Open
Relations always play an important role in the study of topological dynamics. Proximal, distal and almost periodic relations are well studied in literature. We further this direction and analogously study the strongly proximal and weakly d…
View article: On almost periodicity and minimality for semiflows
On almost periodicity and minimality for semiflows Open
In topological dynamics, the dynamical behavior sometimes has a sharp\ncontrast when the action is by semigroups or monoids to when the action is by\ngroups. In this article we bring out this contrast while discussing the\nequivalence of a…
View article: On Almost periodicity and minimality for semiflows
On Almost periodicity and minimality for semiflows Open
In topological dynamics, the dynamical behavior sometimes has a sharp contrast when the action is by semigroups or monoids to when the action is by groups. In this article we bring out this contrast while discussing the equivalence of almo…
View article: On the virtual automorphism group of a minimal flow
On the virtual automorphism group of a minimal flow Open
We introduce the notions ‘virtual automorphism group’ of a minimal flow and ‘semiregular flow’ and investigate the relationship between the virtual and actual group of automorphisms.
View article: Minimality, distality and equicontinuity for semigroup actions on compact Hausdorff spaces
Minimality, distality and equicontinuity for semigroup actions on compact Hausdorff spaces Open
Let $ T $ be any topological semigroup and $ (T, X) $ with phase mapping $ (t, x)\mapsto tx $ a semiflow on a compact $ \text{T}_2 $ space $ X $. If $ tX = X $ for all $ t $ in $ T $ then $ (T, X) $ is called surjective; if $ x\mapsto tx $…
View article: On transitivity dynamics of topological semiflows
On transitivity dynamics of topological semiflows Open
Let $T\times X\rightarrow X, (t,x)\mapsto tx$, be a topological semiflow on a topological space $X$ with phase semigroup $T$. We introduce and discuss in this paper various transitivity dynamics of $(T,X)$.
View article: Minimality, distality and equicontinuity for semigroup actions on compact Hausdorff spaces
Minimality, distality and equicontinuity for semigroup actions on compact Hausdorff spaces Open
Let $π\colon T\times X\rightarrow X$ with phase map $(t,x)\mapsto tx$, denoted $(π,T,X)$, be a \textit{semiflow} on a compact Hausdorff space $X$ with phase semigroup $T$. If each $t\in T$ is onto, $(π,T,X)$ is called surjective; and if ea…
View article: Variations on the concept of topological transitivity
Variations on the concept of topological transitivity Open
We describe various strengthenings of the concept of topological transitivity. Especially when one departs from the family of invertible systems, a number of interesting properties arise. We present the architecture of implications among t…