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Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems

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dc.contributor.author Barnsley, M.F.
dc.contributor.author Vince, A.
dc.date.accessioned 2019-02-13T17:40:20Z
dc.date.available 2019-02-13T17:40:20Z
dc.date.issued 2015
dc.identifier.citation 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. uk_UA
dc.identifier.issn 1815-0659
dc.identifier.other 2010 Mathematics Subject Classification: 05B45; 37B50; 52B50
dc.identifier.other DOI:10.3842/SIGMA.2015.084
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/147148
dc.description.abstract 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. uk_UA
dc.description.sponsorship We thank Alan Carey for interesting discussions and helpful comments. We thank Louisa Barnsley for technical help and suggestions. We thank Krystof Le´sniak, who worked with us on the first version of this paper, namely [3], for many comments and suggestions. We thank the anonymous referees for helpful comments. This work was partially supported by a grant from the Simons Foundation (#322515 to Andrew Vince). It was also partially supported by a grant from the Australian Research Council (#DP130101738). uk_UA
dc.language.iso en uk_UA
dc.publisher Інститут математики НАН України uk_UA
dc.relation.ispartof Symmetry, Integrability and Geometry: Methods and Applications
dc.title Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA


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