论文标题
不严格的吸引人
Pointwise attractors which are not strict
论文作者
论文摘要
我们与Hausdorff空间上连续地图的有限家庭$ \ Mathcal {f} $打交道。如果每个非compact $ compact $ s \ subset u $ a $ a = $ a = \ lim_ {n \ to \ mathcal {f}^n（s）$ a $ a = \ lim_ {n \ to \ lim_ {n \ to \ lim_ {n \ to $ a = n（s）每个严格的吸引子都是一个尖的吸引子，这意味着集合$ \ {x \ in x; \ lim_ {n \ to \ infty} \ mathcal {f}^n（x）= a \} $在其内部包含$ a $。我们介绍了一个点式吸引子的示例 - 从有限集到Sierpiński地毯 - 当我们添加到系统中时，这些示例并不严格。
We deal with the finite family $\mathcal{F}$ of continuous maps on the Hausdorff space. A nonempty compact subset $A$ of such space is called a strict attractor if it has an open neighborhood $U$ such that $A=\lim_{n\to\infty}\mathcal{F}^n(S)$ for every nonempty compact $S\subset U$. Every strict attractor is a pointwise attractor, which means that the set $\{x\in X ; \lim_{n\to\infty}\mathcal{F}^n(x)=A\}$ contains $A$ in its interior. We present a class of examples of pointwise attractors - from the finite set to the Sierpiński carpet - which are not strict when we add to the system one nonexpansive map.
