Density of the level sets of the metric mean dimension for homeomorphisms
Let N be an n-dimensional compact riemannian manifold, with n ≥ 2. In this paper, we prove that for any α ∈ [0, n], the set consisting of homeomorphisms on N with lower and upper metric mean dimensions equal to α is dense in Hom(N). More generally, given α, β ∈ [0, n], with α ≤ β, we show the set co...
- Autores:
-
Muentes Acevedo, Jeovanny de Jesus
Romaña Ibarra, Sergio
Arias Cantillo, Raibel
- 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:20.500.12585/12632
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/12632
https://doi.org/10.1007/s10884-023-10344-5
- Palabra clave:
- Mean dimension
Metric mean dimension
Topological entropy
Genericity
LEMB
- Rights
- openAccess
- License
- http://creativecommons.org/publicdomain/zero/1.0/
| id |
UTB2_2a463b8bc96df113146fb6403679e3f8 |
|---|---|
| oai_identifier_str |
oai:repositorio.utb.edu.co:20.500.12585/12632 |
| network_acronym_str |
UTB2 |
| network_name_str |
Repositorio Institucional UTB |
| repository_id_str |
|
| dc.title.spa.fl_str_mv |
Density of the level sets of the metric mean dimension for homeomorphisms |
| title |
Density of the level sets of the metric mean dimension for homeomorphisms |
| spellingShingle |
Density of the level sets of the metric mean dimension for homeomorphisms Mean dimension Metric mean dimension Topological entropy Genericity LEMB |
| title_short |
Density of the level sets of the metric mean dimension for homeomorphisms |
| title_full |
Density of the level sets of the metric mean dimension for homeomorphisms |
| title_fullStr |
Density of the level sets of the metric mean dimension for homeomorphisms |
| title_full_unstemmed |
Density of the level sets of the metric mean dimension for homeomorphisms |
| title_sort |
Density of the level sets of the metric mean dimension for homeomorphisms |
| dc.creator.fl_str_mv |
Muentes Acevedo, Jeovanny de Jesus Romaña Ibarra, Sergio Arias Cantillo, Raibel |
| dc.contributor.author.none.fl_str_mv |
Muentes Acevedo, Jeovanny de Jesus Romaña Ibarra, Sergio Arias Cantillo, Raibel |
| dc.subject.keywords.spa.fl_str_mv |
Mean dimension Metric mean dimension Topological entropy Genericity |
| topic |
Mean dimension Metric mean dimension Topological entropy Genericity LEMB |
| dc.subject.armarc.none.fl_str_mv |
LEMB |
| description |
Let N be an n-dimensional compact riemannian manifold, with n ≥ 2. In this paper, we prove that for any α ∈ [0, n], the set consisting of homeomorphisms on N with lower and upper metric mean dimensions equal to α is dense in Hom(N). More generally, given α, β ∈ [0, n], with α ≤ β, we show the set consisting of homeomorphisms on N with lower metric mean dimension equal to α and upper metric mean dimension equal to β is dense in Hom(N). Furthermore, we also give a proof that the set of homeomorphisms withupper metric mean dimension equal to n is residual in Hom(N). |
| publishDate |
2023 |
| dc.date.issued.none.fl_str_mv |
2023-12-10 |
| dc.date.accessioned.none.fl_str_mv |
2024-02-12T15:47:28Z |
| dc.date.available.none.fl_str_mv |
2024-02-12T15:47:28Z |
| dc.date.submitted.none.fl_str_mv |
2024-02-12 |
| dc.type.coarversion.fl_str_mv |
http://purl.org/coar/version/c_b1a7d7d4d402bcce |
| dc.type.coar.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/article |
| dc.type.hasversion.spa.fl_str_mv |
info:eu-repo/semantics/draft |
| dc.type.spa.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_6501 |
| status_str |
draft |
| dc.identifier.citation.spa.fl_str_mv |
Acevedo, J.M., Romaña, S. & Arias, R. Density of the Level Sets of the Metric Mean Dimension for Homeomorphisms. J Dyn Diff Equat (2024). https://doi.org/10.1007/s10884-023-10344-5 |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12585/12632 |
| dc.identifier.doi.none.fl_str_mv |
https://doi.org/10.1007/s10884-023-10344-5 |
| dc.identifier.instname.spa.fl_str_mv |
Universidad Tecnológica de Bolívar |
| dc.identifier.reponame.spa.fl_str_mv |
Repositorio Universidad Tecnológica de Bolívar |
| identifier_str_mv |
Acevedo, J.M., Romaña, S. & Arias, R. Density of the Level Sets of the Metric Mean Dimension for Homeomorphisms. J Dyn Diff Equat (2024). https://doi.org/10.1007/s10884-023-10344-5 Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar |
| url |
https://hdl.handle.net/20.500.12585/12632 https://doi.org/10.1007/s10884-023-10344-5 |
| dc.language.iso.spa.fl_str_mv |
eng |
| language |
eng |
| dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
| dc.rights.uri.*.fl_str_mv |
http://creativecommons.org/publicdomain/zero/1.0/ |
| dc.rights.accessrights.spa.fl_str_mv |
info:eu-repo/semantics/openAccess |
| dc.rights.cc.*.fl_str_mv |
CC0 1.0 Universal |
| rights_invalid_str_mv |
http://creativecommons.org/publicdomain/zero/1.0/ CC0 1.0 Universal http://purl.org/coar/access_right/c_abf2 |
| eu_rights_str_mv |
openAccess |
| dc.format.extent.none.fl_str_mv |
14 páginas |
| dc.format.mimetype.spa.fl_str_mv |
application/http |
| dc.publisher.place.spa.fl_str_mv |
Cartagena de Indias |
| dc.publisher.sede.spa.fl_str_mv |
Campus Tecnológico |
| dc.source.spa.fl_str_mv |
Journal of Dynamics and Differential Equations |
| institution |
Universidad Tecnológica de Bolívar |
| bitstream.url.fl_str_mv |
https://repositorio.utb.edu.co/bitstream/20.500.12585/12632/1/s10884-023-10344-5.pdf https://repositorio.utb.edu.co/bitstream/20.500.12585/12632/2/license_rdf https://repositorio.utb.edu.co/bitstream/20.500.12585/12632/3/license.txt https://repositorio.utb.edu.co/bitstream/20.500.12585/12632/4/s10884-023-10344-5.pdf.txt https://repositorio.utb.edu.co/bitstream/20.500.12585/12632/5/s10884-023-10344-5.pdf.jpg |
| bitstream.checksum.fl_str_mv |
7faca5224c9a40957a7c694e0f6a0c83 42fd4ad1e89814f5e4a476b409eb708c e20ad307a1c5f3f25af9304a7a7c86b6 b044dcf907cad55b35ef3a62bdca150c 774f853fb6aa20486c8e0171f446d8cf |
| bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 |
| repository.name.fl_str_mv |
Repositorio Institucional UTB |
| repository.mail.fl_str_mv |
repositorioutb@utb.edu.co |
| _version_ |
1814021789949362176 |
| spelling |
Muentes Acevedo, Jeovanny de Jesusec5c0208-d53f-44d4-a347-fdb3d28db2abRomaña Ibarra, Sergio246f5889-e109-4574-bb68-7bb66e7f17c7Arias Cantillo, Raibel84adec42-1fd2-44b8-8e80-5f44485619c12024-02-12T15:47:28Z2024-02-12T15:47:28Z2023-12-102024-02-12Acevedo, J.M., Romaña, S. & Arias, R. Density of the Level Sets of the Metric Mean Dimension for Homeomorphisms. J Dyn Diff Equat (2024). https://doi.org/10.1007/s10884-023-10344-5https://hdl.handle.net/20.500.12585/12632https://doi.org/10.1007/s10884-023-10344-5Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarLet N be an n-dimensional compact riemannian manifold, with n ≥ 2. In this paper, we prove that for any α ∈ [0, n], the set consisting of homeomorphisms on N with lower and upper metric mean dimensions equal to α is dense in Hom(N). More generally, given α, β ∈ [0, n], with α ≤ β, we show the set consisting of homeomorphisms on N with lower metric mean dimension equal to α and upper metric mean dimension equal to β is dense in Hom(N). Furthermore, we also give a proof that the set of homeomorphisms withupper metric mean dimension equal to n is residual in Hom(N).14 páginasapplication/httpenghttp://creativecommons.org/publicdomain/zero/1.0/info:eu-repo/semantics/openAccessCC0 1.0 Universalhttp://purl.org/coar/access_right/c_abf2Journal of Dynamics and Differential EquationsDensity of the level sets of the metric mean dimension for homeomorphismsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/drafthttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/version/c_b1a7d7d4d402bccehttp://purl.org/coar/resource_type/c_2df8fbb1Mean dimensionMetric mean dimensionTopological entropyGenericityLEMBCartagena de IndiasCampus TecnológicoPúblico generalAcevedo, J.M., Romaña, S., Arias, R.: Hölder continuous maps on the interval with positive metric mean dimension. Rev. Colomb. de Math. 57, 57–76 (2024)Acevedo, J.M.: Genericity of continuous maps with positive metric mean dimension. RM 77(1), 2 (2022)Acevedo, J.M., Baraviera, A., Becker, A.J., Scopel É.: Metric mean dimension and mean Hausdorff dimension varying the metric. (2024)Artin M., Mazur B.: On periodic points. Ann. Math. pp. 82-99 (1965)Carvalho, M., Rodrigues, F.B., Varandas, P.: Generic homeomorphisms have full metric mean dimension. Ergodic Theory Dynam. Syst. 42(1), 40–64 (2022)Gutman, Y., Tsukamoto, M.: Embedding minimal dynamical systems into Hilbert cubes. Invent. Math. 221(1), 113–166 (2020)Hurley, M.: On proofs of the general density theorem. Proceed. Amer. Math. Soci. 124(4), 1305–1309 (1996)Lindenstrauss, E., Weiss, B.: Mean topological dimension. Israel J. Math. 115(1), 1–24 (2000)Lindenstrauss, E., Tsukamoto, M.: Double variational principle for mean dimension. Geom. Funct. Anal. 29(4), 1048–1109 (2019)Lindenstrauss, E., Tsukamoto, M.: From rate distortion theory to metric mean dimension: variational principle. IEEE Trans. Inf. Theory 64(5), 3590–3609 (2018)Lindenstrauss, E., Tsukamoto, M.: Mean dimension and an embedding problem: an example. Israel J. Math. 199(2), 573–584 (2014)Shinoda, M., Tsukamoto, M.: Symbolic dynamics in mean dimension theory. Ergodic Theory Dynam. Syst. 41(8), 2542–2560 (2021)Tsukamoto, M.: Mean dimension of full shifts. Israel J. Math. 230, 183–193 (2019)Velozo A., Velozo R.: Rate distortion theory, metric mean dimension and measure theoretic entropy. arXiv preprint arXiv:1707.05762 (2017)Yano, K.: A remark on the topological entropy of homeomorphisms. Invent. Math. 59(3), 215–220 (1980)http://purl.org/coar/resource_type/c_2df8fbb1ORIGINALs10884-023-10344-5.pdfs10884-023-10344-5.pdfArtículo principalapplication/pdf547836https://repositorio.utb.edu.co/bitstream/20.500.12585/12632/1/s10884-023-10344-5.pdf7faca5224c9a40957a7c694e0f6a0c83MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8701https://repositorio.utb.edu.co/bitstream/20.500.12585/12632/2/license_rdf42fd4ad1e89814f5e4a476b409eb708cMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-83182https://repositorio.utb.edu.co/bitstream/20.500.12585/12632/3/license.txte20ad307a1c5f3f25af9304a7a7c86b6MD53TEXTs10884-023-10344-5.pdf.txts10884-023-10344-5.pdf.txtExtracted texttext/plain31336https://repositorio.utb.edu.co/bitstream/20.500.12585/12632/4/s10884-023-10344-5.pdf.txtb044dcf907cad55b35ef3a62bdca150cMD54THUMBNAILs10884-023-10344-5.pdf.jpgs10884-023-10344-5.pdf.jpgGenerated Thumbnailimage/jpeg6289https://repositorio.utb.edu.co/bitstream/20.500.12585/12632/5/s10884-023-10344-5.pdf.jpg774f853fb6aa20486c8e0171f446d8cfMD5520.500.12585/12632oai:repositorio.utb.edu.co:20.500.12585/126322024-02-14 00:16:50.11Repositorio Institucional UTBrepositorioutb@utb.edu.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 |