Hölder continuous maps on the interval with positive metric mean dimension
Fix a compact metric space X with finite topological dimension. Let C0(X) be the space of continuous maps on X and Hα(X) the space of α-Hölder continuous maps on X, for α ∈ (0, 1]. Let H1(X) be the space of Lipschitz continuous maps on X. We have H1(X) ⊂ Hβ(X) ⊂ Hα(X) ⊂ C0(X), where 0 < α < β...
- Autores:
-
Muentes Acevedo, Jeovanny de Jesus
Romana Ibarra, Sergio Augusto
Arias Cantillo, Raibel de Jesús
- Tipo de recurso:
- Fecha de publicación:
- 2023
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/12603
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/12603
https://doi.org/10.15446/recolma.v57nSupl.112448
- Palabra clave:
- Metric mean dimension
Topological entropy
Hölder continuous maps
LEMB
- Rights
- openAccess
- License
- http://creativecommons.org/publicdomain/zero/1.0/
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| dc.title.spa.fl_str_mv |
Hölder continuous maps on the interval with positive metric mean dimension |
| dc.title.alternative.spa.fl_str_mv |
Funciones Hölder continuas en el intervalo con dimensión métrica media positiva |
| title |
Hölder continuous maps on the interval with positive metric mean dimension |
| spellingShingle |
Hölder continuous maps on the interval with positive metric mean dimension Metric mean dimension Topological entropy Hölder continuous maps LEMB |
| title_short |
Hölder continuous maps on the interval with positive metric mean dimension |
| title_full |
Hölder continuous maps on the interval with positive metric mean dimension |
| title_fullStr |
Hölder continuous maps on the interval with positive metric mean dimension |
| title_full_unstemmed |
Hölder continuous maps on the interval with positive metric mean dimension |
| title_sort |
Hölder continuous maps on the interval with positive metric mean dimension |
| dc.creator.fl_str_mv |
Muentes Acevedo, Jeovanny de Jesus Romana Ibarra, Sergio Augusto Arias Cantillo, Raibel de Jesús |
| dc.contributor.author.none.fl_str_mv |
Muentes Acevedo, Jeovanny de Jesus Romana Ibarra, Sergio Augusto Arias Cantillo, Raibel de Jesús |
| dc.subject.keywords.spa.fl_str_mv |
Metric mean dimension Topological entropy Hölder continuous maps |
| topic |
Metric mean dimension Topological entropy Hölder continuous maps LEMB |
| dc.subject.armarc.none.fl_str_mv |
LEMB |
| description |
Fix a compact metric space X with finite topological dimension. Let C0(X) be the space of continuous maps on X and Hα(X) the space of α-Hölder continuous maps on X, for α ∈ (0, 1]. Let H1(X) be the space of Lipschitz continuous maps on X. We have H1(X) ⊂ Hβ(X) ⊂ Hα(X) ⊂ C0(X), where 0 < α < β < 1. It is well-known that if φ ∈ H1(X), then φ has metric mean dimension equal to zero. On the other hand, if X is a manifold, then C0(X) contains a residual subset whose elements have positive metric mean dimension. In this work we will prove that, for any α ∈ (0, 1), there exists φ ∈ Hα([0, 1]) with positive metric mean dimension. |
| publishDate |
2023 |
| dc.date.issued.none.fl_str_mv |
2023-11 |
| dc.date.accessioned.none.fl_str_mv |
2024-02-01T20:28:36Z |
| dc.date.available.none.fl_str_mv |
2024-02-01T20:28:36Z |
| dc.date.submitted.none.fl_str_mv |
2024-02-01 |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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info:eu-repo/semantics/article |
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info:eu-repo/semantics/publishedVersion |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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publishedVersion |
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Muentes Acevedo, J. de J., Romaña Ibarra, S. A. y Arias Cantillo, R. de J. (2024). Hölder continuous maps on the interval with positive metric mean dimension. Revista Colombiana de Matemáticas, 57(Supl), 57–76. https://doi.org/10.15446/recolma.v57nSupl.112448 |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12585/12603 |
| dc.identifier.doi.none.fl_str_mv |
https://doi.org/10.15446/recolma.v57nSupl.112448 |
| dc.identifier.instname.spa.fl_str_mv |
Universidad Tecnológica de Bolívar |
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Repositorio Universidad Tecnológica de Bolívar |
| identifier_str_mv |
Muentes Acevedo, J. de J., Romaña Ibarra, S. A. y Arias Cantillo, R. de J. (2024). Hölder continuous maps on the interval with positive metric mean dimension. Revista Colombiana de Matemáticas, 57(Supl), 57–76. https://doi.org/10.15446/recolma.v57nSupl.112448 Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar |
| url |
https://hdl.handle.net/20.500.12585/12603 https://doi.org/10.15446/recolma.v57nSupl.112448 |
| dc.language.iso.spa.fl_str_mv |
eng |
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eng |
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http://purl.org/coar/access_right/c_abf2 |
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info:eu-repo/semantics/openAccess |
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CC0 1.0 Universal |
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http://creativecommons.org/publicdomain/zero/1.0/ CC0 1.0 Universal http://purl.org/coar/access_right/c_abf2 |
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openAccess |
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20 páginas |
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Cartagena de Indias |
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Campus Tecnológico |
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Revista Colombiana de Matemáticas |
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Universidad Tecnológica de Bolívar |
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Muentes Acevedo, Jeovanny de Jesusec5c0208-d53f-44d4-a347-fdb3d28db2abRomana Ibarra, Sergio Augustod6a5ca18-f706-412b-a6b8-9c0527029c68Arias Cantillo, Raibel de Jesús84adec42-1fd2-44b8-8e80-5f44485619c12024-02-01T20:28:36Z2024-02-01T20:28:36Z2023-112024-02-01Muentes Acevedo, J. de J., Romaña Ibarra, S. A. y Arias Cantillo, R. de J. (2024). Hölder continuous maps on the interval with positive metric mean dimension. Revista Colombiana de Matemáticas, 57(Supl), 57–76. https://doi.org/10.15446/recolma.v57nSupl.112448https://hdl.handle.net/20.500.12585/12603https://doi.org/10.15446/recolma.v57nSupl.112448Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarFix a compact metric space X with finite topological dimension. Let C0(X) be the space of continuous maps on X and Hα(X) the space of α-Hölder continuous maps on X, for α ∈ (0, 1]. Let H1(X) be the space of Lipschitz continuous maps on X. We have H1(X) ⊂ Hβ(X) ⊂ Hα(X) ⊂ C0(X), where 0 < α < β < 1. It is well-known that if φ ∈ H1(X), then φ has metric mean dimension equal to zero. On the other hand, if X is a manifold, then C0(X) contains a residual subset whose elements have positive metric mean dimension. In this work we will prove that, for any α ∈ (0, 1), there exists φ ∈ Hα([0, 1]) with positive metric mean dimension.20 páginasapplication/pdfenghttp://creativecommons.org/publicdomain/zero/1.0/info:eu-repo/semantics/openAccessCC0 1.0 Universalhttp://purl.org/coar/access_right/c_abf2Revista Colombiana de MatemáticasHölder continuous maps on the interval with positive metric mean dimensionFunciones Hölder continuas en el intervalo con dimensión métrica media positivainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Metric mean dimensionTopological entropyHölder continuous mapsLEMBCartagena de IndiasCampus TecnológicoPúblico generalJ. Muentes Acevedo, Genericity of continuous maps with positive metric mean dimension, Results in Mathematics 77 (2022), no. 1, 2.Carvalho, B. Fagner Rodrigues, and P. Varandas, Generic homeomor phisms have full metric mean dimension, Ergodic Theory and Dynamical Systems 42 (2022), no. 1, 40–64.P. Hazard, Maps in dimension one with infinite entropy, Arkiv för Matematik 58 (2020), no. 1, 95–119.A. Katok and B. Hasselblatt, Introduction to the modern theory of dynamical systems, vol. 54, Cambridge university press, 1997.S. Kolyada and S. Lubomir, Topological entropy of nonautonomous dynamical systems, Random and computational dynamics 4 (1996), no. 2, 205.E. Lindenstrauss and B. Weiss, Mean topological dimension, Israel Journal of Mathematics 115 (2000), no. 1, 1–24.W. De Melo and S. Van Strien, One-dimensional dynamics, Springer Science & Business Media 25 (2012).M. Misiurewicz, Horseshoes for continuous mappings of an interval, Dynamical systems. Springer, Berlin, Heidelberg, 2010.A. Velozo and R. Velozo, Rate distortion theory, metric mean dimension and measure theoretic entropy, arXiv preprint arXiv:1707.05762, 2017.http://purl.org/coar/resource_type/c_2df8fbb1ORIGINALace-rom-ari.pdface-rom-ari.pdfArtículo principalapplication/pdf540224https://repositorio.utb.edu.co/bitstream/20.500.12585/12603/1/ace-rom-ari.pdf4f0efab8df3e52184e353f64e072b34bMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8701https://repositorio.utb.edu.co/bitstream/20.500.12585/12603/2/license_rdf42fd4ad1e89814f5e4a476b409eb708cMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-83182https://repositorio.utb.edu.co/bitstream/20.500.12585/12603/3/license.txte20ad307a1c5f3f25af9304a7a7c86b6MD53TEXTace-rom-ari.pdf.txtace-rom-ari.pdf.txtExtracted texttext/plain36767https://repositorio.utb.edu.co/bitstream/20.500.12585/12603/4/ace-rom-ari.pdf.txt2a82747e97aabd5d44113ba8dece04c2MD54THUMBNAILace-rom-ari.pdf.jpgace-rom-ari.pdf.jpgGenerated 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