Fractal and Hausdorff dimensions for systems of iterative functional equations
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | |
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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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 info:eu-repo/semantics/openAccess |
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metadata only access |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
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) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799133459828965376 |