Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems
The fast basin of an attractor of an iterated function system (IFS) is the set of points in the domain of the IFS whose orbits under the associated semigroup intersect the attractor. Fast basins can have non-integer dimension and comprise a class of deterministic fractal sets. The relationship betwe...
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| Дата: | 2015 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2015
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147148 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems / M.F. Barnsley, A. Vince // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 17 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1471482019-02-14T01:25:47Z Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems Barnsley, M.F. Vince, A. The fast basin of an attractor of an iterated function system (IFS) is the set of points in the domain of the IFS whose orbits under the associated semigroup intersect the attractor. Fast basins can have non-integer dimension and comprise a class of deterministic fractal sets. The relationship between the basin and the fast basin of a point-fibred attractor is analyzed. To better understand the topology and geometry of fast basins, and because of analogies with analytic continuation, branched fractal manifolds are introduced. A branched fractal manifold is a metric space constructed from the extended code space of a point-fibred attractor, by identifying some addresses. Typically, a branched fractal manifold is a union of a nondenumerable collection of nonhomeomorphic objects, isometric copies of generalized fractal blowups of the attractor. 2015 Article Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems / M.F. Barnsley, A. Vince // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 17 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 05B45; 37B50; 52B50 DOI:10.3842/SIGMA.2015.084 http://dspace.nbuv.gov.ua/handle/123456789/147148 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The fast basin of an attractor of an iterated function system (IFS) is the set of points in the domain of the IFS whose orbits under the associated semigroup intersect the attractor. Fast basins can have non-integer dimension and comprise a class of deterministic fractal sets. The relationship between the basin and the fast basin of a point-fibred attractor is analyzed. To better understand the topology and geometry of fast basins, and because of analogies with analytic continuation, branched fractal manifolds are introduced. A branched fractal manifold is a metric space constructed from the extended code space of a point-fibred attractor, by identifying some addresses. Typically, a branched fractal manifold is a union of a nondenumerable collection of nonhomeomorphic objects, isometric copies of generalized fractal blowups of the attractor. |
| format |
Article |
| author |
Barnsley, M.F. Vince, A. |
| spellingShingle |
Barnsley, M.F. Vince, A. Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Barnsley, M.F. Vince, A. |
| author_sort |
Barnsley, M.F. |
| title |
Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems |
| title_short |
Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems |
| title_full |
Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems |
| title_fullStr |
Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems |
| title_full_unstemmed |
Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems |
| title_sort |
fast basins and branched fractal manifolds of attractors of iterated function systems |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147148 |
| citation_txt |
Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems / M.F. Barnsley, A. Vince // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 17 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:26:42Z |
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