Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems
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| Creator |
Barnsley, M.F.
Vince, A. |
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| 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.
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| Date |
2019-02-13T17:40:20Z
2019-02-13T17:40:20Z 2015 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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