ﻻ يوجد ملخص باللغة العربية
Let $X$ be a non-degenerate connected compact metric space. If $X$ admits a distal minimal action by a finitely generated amenable group, then the first vCech cohomology group $ {check H}^1(X)$ with integer coefficients is nontrivial. In particular, if $X$ is homotopically equivalent to a CW complex, then $X$ cannot be simply connected.
We show that if $G$ is a finitely generated group of subexponential growth and $X$ is a Suslinian continuum, then any action of $G$ on $X$ cannot be expansive.
Let $Gamma$ be a lattice in ${rm SL}(n, mathbb R)$ with $ngeq 3$ and $mathcal S$ be a closed surface. Then $Gamma$ has no distal minimal action on $mathcal S$.
The paper offers a thorough study of multiorders and their applications to measure-preserving actions of countable amenable groups. By a multiorder on a countable group we mean any probability measure $ u$ on the collection $mathcal O$ of linear orde
In this paper, we study discrete spectrum of invariant measures for countable discrete amenable group actions. We show that an invariant measure has discrete spectrum if and only if it has bounded measure complexity. We also prove that, discrete sp
Let $X$ be a Peano continuum having a free arc and let $C^0(X)$ be the semigroup of continuous self-maps of $X$. A subsemigroup $Fsubset C^0(X)$ is said to be sensitive, if there is some constant $c>0$ such that for any nonempty open set $Usubset X$,