Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2111.01927 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915088186736640 |
|---|---|
| author | Klinga, Paweł Kwela, Adam |
| author_facet | Klinga, Paweł Kwela, Adam |
| contents | This paper is another attempt to measure the difference between the family $A[0,1]$ of attractors for iterated function systems acting on $[0,1]$ and a broader family, the set $A_w[0,1]$ of attractors for weak iterated function systems acting on $[0,1]$.
It is known that both $A[0,1]$ and $A_w[0,1]$ are meager subsets of the hyperspace $K([0,1])$ (of all compact subsets of $[0,1]$ equipped in the Hausdorff metric). Actually, $A[0,1]$ is even $σ$-lower porous while the question about $σ$-lower porosity of $A_w[0,1]$ is still open.
We prove that $A[0,1]$ is not $σ$-strongly porous in $K([0,1])$. Moreover, we show that $A_w[0,1]\setminus A[0,1]$ is dense in $K([0,1])$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_01927 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Porosities of the sets of attractors Klinga, Paweł Kwela, Adam Dynamical Systems General Topology This paper is another attempt to measure the difference between the family $A[0,1]$ of attractors for iterated function systems acting on $[0,1]$ and a broader family, the set $A_w[0,1]$ of attractors for weak iterated function systems acting on $[0,1]$. It is known that both $A[0,1]$ and $A_w[0,1]$ are meager subsets of the hyperspace $K([0,1])$ (of all compact subsets of $[0,1]$ equipped in the Hausdorff metric). Actually, $A[0,1]$ is even $σ$-lower porous while the question about $σ$-lower porosity of $A_w[0,1]$ is still open. We prove that $A[0,1]$ is not $σ$-strongly porous in $K([0,1])$. Moreover, we show that $A_w[0,1]\setminus A[0,1]$ is dense in $K([0,1])$. |
| title | Porosities of the sets of attractors |
| topic | Dynamical Systems General Topology |
| url | https://arxiv.org/abs/2111.01927 |