Fractal and Hausdorff dimensions for systems of iterative functional equations

Detalhes bibliográficos
Autor(a) principal: Buescu, Jorge
Data de Publicação: 2019
Outros Autores: Serpa, Cristina
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.21/11017
Resumo: We consider systems of non-affine iterative functional equations. From the constructive form of the solutions, recently established by the authors, representations of these systems in terms of symbolic spaces as well as associated fractal structures are constructed. These results are then used to derive upper bounds both for the appropriate fractal dimension and the corresponding Hausdorff dimension of solutions. Using the formalism of iterated function systems, we obtain a sharp result on the Hausdorff dimension in terms of the corresponding fractal structures. The connections of our results with related objects known in the literature, including Girgensohn functions, fractal interpolation functions and Weierstrass functions, are established.
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spelling Fractal and Hausdorff dimensions for systems of iterative functional equationsFractal structureHausdorff dimensionFractal dimensionSymbolic spaceFractal interpolation functionSystem of iterative functional equationsWe consider systems of non-affine iterative functional equations. From the constructive form of the solutions, recently established by the authors, representations of these systems in terms of symbolic spaces as well as associated fractal structures are constructed. These results are then used to derive upper bounds both for the appropriate fractal dimension and the corresponding Hausdorff dimension of solutions. Using the formalism of iterated function systems, we obtain a sharp result on the Hausdorff dimension in terms of the corresponding fractal structures. The connections of our results with related objects known in the literature, including Girgensohn functions, fractal interpolation functions and Weierstrass functions, are established.ElsevierRCIPLBuescu, JorgeSerpa, Cristina2020-01-21T15:14:46Z2019-12-152019-12-15T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/11017engBUESCU, Jorge; SERPA, Cristina – Fractal and Hausdorff dimensions for systems of iterative functional equations. Journal of Mathematical Analysis and Applications. ISSN 0022-247X. Vol. 480, N.º 2 (2019), pp. 1-190022-247X10.1016/j.jmaa.2019.123429metadata only accessinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-08-03T10:01:45Zoai:repositorio.ipl.pt:10400.21/11017Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:19:21.313127Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Fractal and Hausdorff dimensions for systems of iterative functional equations
title Fractal and Hausdorff dimensions for systems of iterative functional equations
spellingShingle Fractal and Hausdorff dimensions for systems of iterative functional equations
Buescu, Jorge
Fractal structure
Hausdorff dimension
Fractal dimension
Symbolic space
Fractal interpolation function
System of iterative functional equations
title_short Fractal and Hausdorff dimensions for systems of iterative functional equations
title_full Fractal and Hausdorff dimensions for systems of iterative functional equations
title_fullStr Fractal and Hausdorff dimensions for systems of iterative functional equations
title_full_unstemmed Fractal and Hausdorff dimensions for systems of iterative functional equations
title_sort Fractal and Hausdorff dimensions for systems of iterative functional equations
author Buescu, Jorge
author_facet Buescu, Jorge
Serpa, Cristina
author_role author
author2 Serpa, Cristina
author2_role author
dc.contributor.none.fl_str_mv RCIPL
dc.contributor.author.fl_str_mv Buescu, Jorge
Serpa, Cristina
dc.subject.por.fl_str_mv Fractal structure
Hausdorff dimension
Fractal dimension
Symbolic space
Fractal interpolation function
System of iterative functional equations
topic Fractal structure
Hausdorff dimension
Fractal dimension
Symbolic space
Fractal interpolation function
System of iterative functional equations
description We consider systems of non-affine iterative functional equations. From the constructive form of the solutions, recently established by the authors, representations of these systems in terms of symbolic spaces as well as associated fractal structures are constructed. These results are then used to derive upper bounds both for the appropriate fractal dimension and the corresponding Hausdorff dimension of solutions. Using the formalism of iterated function systems, we obtain a sharp result on the Hausdorff dimension in terms of the corresponding fractal structures. The connections of our results with related objects known in the literature, including Girgensohn functions, fractal interpolation functions and Weierstrass functions, are established.
publishDate 2019
dc.date.none.fl_str_mv 2019-12-15
2019-12-15T00:00:00Z
2020-01-21T15:14:46Z
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://hdl.handle.net/10400.21/11017
url http://hdl.handle.net/10400.21/11017
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv BUESCU, Jorge; SERPA, Cristina – Fractal and Hausdorff dimensions for systems of iterative functional equations. Journal of Mathematical Analysis and Applications. ISSN 0022-247X. Vol. 480, N.º 2 (2019), pp. 1-19
0022-247X
10.1016/j.jmaa.2019.123429
dc.rights.driver.fl_str_mv metadata only access
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dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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