"Pointwise attractors which are not strict"Nowak, MagdalenaWe deal with the Barnsley-Huthinson operator $\mathcal{F}$ associated with the finite family of continuous maps on the normal Hausdorff space. Each 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 which are not strict - from the finite set to the Sierpinski carpet. |
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