ﻻ يوجد ملخص باللغة العربية
Let $X$ be a regular curve and $n$ be a positive integer such that for every nonempty open set $Usubset X$, there is a nonempty connected open set $Vsubset U$ with the cardinality $|partial_X(V)|leq n$. We show that if $X$ admits a sensitive action of a group $G$, then $G$ contains a free subsemigroup and the action has positive geometric entropy. As a corollary, $X$ admits no sensitive nilpotent group action.
Let $G$ be a countable group and $X$ be a totally regular curve. Suppose that $phi:Grightarrow {rm Homeo}(X)$ is a minimal action. Then we show an alternative: either the action is topologically conjugate to isometries on the circle $mathbb S^1$ (thi
In ergodic theory, given sufficient conditions on the system, every weak mixing $mathbb{N}$-action is strong mixing along a density one subset of $mathbb{N}$. We ask if a similar statement holds in topological dynamics with density one replaced with
In this paper, we study a natural class of groups that act as affine transformations of $mathbb T^N$. We investigate whether these solvable, abelian-by-cyclic, groups can act smoothly and nonaffinely on $mathbb T^N$ while remaining homotopic to the a
We show that group actions on many treelike compact spaces are not too complicated dynamically. We first observe that an old argument of Seidler implies that every action of a topological group $G$ on a regular continuum is null and therefore also ta
In this paper we study chaotic behavior of actions of a countable discrete group acting on a compact metric space by self-homeomorphisms. For actions of a countable discrete group G, we introduce local weak mixing and Li-Yorke chaos; and prove that