Thresholds for one-parameter families of affine iterated function systems
This paper examines thresholds for certain properties of the attractor of a general one-parameter affine family of iterated functions systems. As the parameter increases, the iterated function system becomes less contractive, and the attractor evolves. Thresholds are studied for the following proper...
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| Published in | Nonlinearity Vol. 33; no. 12; pp. 6541 - 6563 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
01.12.2020
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| Online Access | Get full text |
| ISSN | 0951-7715 1361-6544 |
| DOI | 10.1088/1361-6544/aba237 |
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| Summary: | This paper examines thresholds for certain properties of the attractor of a general one-parameter affine family of iterated functions systems. As the parameter increases, the iterated function system becomes less contractive, and the attractor evolves. Thresholds are studied for the following properties: the existence of an attractor, the connectivity of the attractor, and the existence of non-empty interior of the attractor. Also discussed are transition phenomena between existence and non-existence of an attractor. |
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| ISSN: | 0951-7715 1361-6544 |
| DOI: | 10.1088/1361-6544/aba237 |