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Coding of substitution dynamical systems as shifts of finite type

Bibliographic Details
Main Author: Surer, Paul [UNESP]
Publication Date: 2016
Format: Article
Language: eng
Source: Repositório Institucional da UNESP
Download full: http://dx.doi.org/10.1017/etds.2014.80
http://hdl.handle.net/11449/172953
Summary: We develop a theory that allows us to code dynamical systems induced by primitive substitutions continuously as shifts of finite type in many different ways. The well-known prefix-suffix coding turns out to correspond to one special case. We precisely analyse the basic properties of these codings (injectivity, coding of the periodic points, properties of the presentation graph, interaction with the shift map). A lot of examples illustrate the theory and show that, depending on the particular coding, several amazing effects may occur. The results give new insights into the theory of substitution dynamical systems and might serve as a powerful tool for further researches.
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spelling Coding of substitution dynamical systems as shifts of finite typeWe develop a theory that allows us to code dynamical systems induced by primitive substitutions continuously as shifts of finite type in many different ways. The well-known prefix-suffix coding turns out to correspond to one special case. We precisely analyse the basic properties of these codings (injectivity, coding of the periodic points, properties of the presentation graph, interaction with the shift map). A lot of examples illustrate the theory and show that, depending on the particular coding, several amazing effects may occur. The results give new insights into the theory of substitution dynamical systems and might serve as a powerful tool for further researches.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Departamento de Matemática IBILCE - UNESPDepartamento de Matemática IBILCE - UNESPFAPESP: 2009/07744-0Universidade Estadual Paulista (Unesp)Surer, Paul [UNESP]2018-12-11T17:02:52Z2018-12-11T17:02:52Z2016-05-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article944-972application/pdfhttp://dx.doi.org/10.1017/etds.2014.80Ergodic Theory and Dynamical Systems, v. 36, n. 3, p. 944-972, 2016.1469-44170143-3857http://hdl.handle.net/11449/17295310.1017/etds.2014.802-s2.0-849685725712-s2.0-84968572571.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengErgodic Theory and Dynamical Systems1,1931,193info:eu-repo/semantics/openAccess2024-11-01T14:27:12Zoai:repositorio.unesp.br:11449/172953Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462024-11-01T14:27:12Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Coding of substitution dynamical systems as shifts of finite type
title Coding of substitution dynamical systems as shifts of finite type
spellingShingle Coding of substitution dynamical systems as shifts of finite type
Surer, Paul [UNESP]
title_short Coding of substitution dynamical systems as shifts of finite type
title_full Coding of substitution dynamical systems as shifts of finite type
title_fullStr Coding of substitution dynamical systems as shifts of finite type
title_full_unstemmed Coding of substitution dynamical systems as shifts of finite type
title_sort Coding of substitution dynamical systems as shifts of finite type
author Surer, Paul [UNESP]
author_facet Surer, Paul [UNESP]
author_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Surer, Paul [UNESP]
description We develop a theory that allows us to code dynamical systems induced by primitive substitutions continuously as shifts of finite type in many different ways. The well-known prefix-suffix coding turns out to correspond to one special case. We precisely analyse the basic properties of these codings (injectivity, coding of the periodic points, properties of the presentation graph, interaction with the shift map). A lot of examples illustrate the theory and show that, depending on the particular coding, several amazing effects may occur. The results give new insights into the theory of substitution dynamical systems and might serve as a powerful tool for further researches.
publishDate 2016
dc.date.none.fl_str_mv 2016-05-01
2018-12-11T17:02:52Z
2018-12-11T17:02:52Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1017/etds.2014.80
Ergodic Theory and Dynamical Systems, v. 36, n. 3, p. 944-972, 2016.
1469-4417
0143-3857
http://hdl.handle.net/11449/172953
10.1017/etds.2014.80
2-s2.0-84968572571
2-s2.0-84968572571.pdf
url http://dx.doi.org/10.1017/etds.2014.80
http://hdl.handle.net/11449/172953
identifier_str_mv Ergodic Theory and Dynamical Systems, v. 36, n. 3, p. 944-972, 2016.
1469-4417
0143-3857
10.1017/etds.2014.80
2-s2.0-84968572571
2-s2.0-84968572571.pdf
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Ergodic Theory and Dynamical Systems
1,193
1,193
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 944-972
application/pdf
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv repositoriounesp@unesp.br
_version_ 1834483474929549312

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