2025-02-23T09:13:32-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: Query fl=%2A&wt=json&json.nl=arrarr&q=id%3A%22irk-123456789-147148%22&qt=morelikethis&rows=5
2025-02-23T09:13:32-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: => GET http://localhost:8983/solr/biblio/select?fl=%2A&wt=json&json.nl=arrarr&q=id%3A%22irk-123456789-147148%22&qt=morelikethis&rows=5
2025-02-23T09:13:32-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: <= 200 OK
2025-02-23T09:13:32-05:00 DEBUG: Deserialized SOLR response
Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems

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...

Full description

Saved in:
Bibliographic Details
Main Authors: Barnsley, M.F., Vince, A.
Format: Article
Language:English
Published: Інститут математики НАН України 2015
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/147148
Tags: Add Tag
No Tags, Be the first to tag this record!
id irk-123456789-147148
record_format dspace
spelling 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
work_keys_str_mv AT barnsleymf fastbasinsandbranchedfractalmanifoldsofattractorsofiteratedfunctionsystems
AT vincea fastbasinsandbranchedfractalmanifoldsofattractorsofiteratedfunctionsystems
first_indexed 2023-05-20T17:26:42Z
last_indexed 2023-05-20T17:26:42Z
_version_ 1796153310658428928

Similar Items