Mean Dimension and Metric Mean Dimension for Non-autonomous Dynamical Systems
In this paper we extend the definitions of mean dimension and metric mean dimension for non-autonomous dynamical systems. We show some properties of this extension and furthermore some applications to the mean dimension and metric mean dimension of single continuous maps.
- Autores:
-
Rodrigues, Fagner B.
Muentes Acevedo, Jeovanny
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/10338
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/10338
https://doi.org/10.1007/s10883-021-09541-6
- Palabra clave:
- Non-autonomous dynamical systems
Mean dimension
Metric mean dimension
Topological entropy
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
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| dc.title.spa.fl_str_mv |
Mean Dimension and Metric Mean Dimension for Non-autonomous Dynamical Systems |
| title |
Mean Dimension and Metric Mean Dimension for Non-autonomous Dynamical Systems |
| spellingShingle |
Mean Dimension and Metric Mean Dimension for Non-autonomous Dynamical Systems Non-autonomous dynamical systems Mean dimension Metric mean dimension Topological entropy |
| title_short |
Mean Dimension and Metric Mean Dimension for Non-autonomous Dynamical Systems |
| title_full |
Mean Dimension and Metric Mean Dimension for Non-autonomous Dynamical Systems |
| title_fullStr |
Mean Dimension and Metric Mean Dimension for Non-autonomous Dynamical Systems |
| title_full_unstemmed |
Mean Dimension and Metric Mean Dimension for Non-autonomous Dynamical Systems |
| title_sort |
Mean Dimension and Metric Mean Dimension for Non-autonomous Dynamical Systems |
| dc.creator.fl_str_mv |
Rodrigues, Fagner B. Muentes Acevedo, Jeovanny |
| dc.contributor.author.none.fl_str_mv |
Rodrigues, Fagner B. Muentes Acevedo, Jeovanny |
| dc.subject.keywords.spa.fl_str_mv |
Non-autonomous dynamical systems Mean dimension Metric mean dimension Topological entropy |
| topic |
Non-autonomous dynamical systems Mean dimension Metric mean dimension Topological entropy |
| description |
In this paper we extend the definitions of mean dimension and metric mean dimension for non-autonomous dynamical systems. We show some properties of this extension and furthermore some applications to the mean dimension and metric mean dimension of single continuous maps. |
| publishDate |
2020 |
| dc.date.issued.none.fl_str_mv |
2020-10-07 |
| dc.date.accessioned.none.fl_str_mv |
2021-07-29T19:26:35Z |
| dc.date.available.none.fl_str_mv |
2021-07-29T19:26:35Z |
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2021-07-29 |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.identifier.citation.spa.fl_str_mv |
Rodrigues, F.B., Acevedo, J.M. Mean Dimension and Metric Mean Dimension for Non-autonomous Dynamical Systems. J Dyn Control Syst (2021). https://doi.org/10.1007/s10883-021-09541-6 |
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https://hdl.handle.net/20.500.12585/10338 |
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https://doi.org/10.1007/s10883-021-09541-6 |
| dc.identifier.instname.spa.fl_str_mv |
Universidad Tecnológica de Bolívar |
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Repositorio Universidad Tecnológica de Bolívar |
| identifier_str_mv |
Rodrigues, F.B., Acevedo, J.M. Mean Dimension and Metric Mean Dimension for Non-autonomous Dynamical Systems. J Dyn Control Syst (2021). https://doi.org/10.1007/s10883-021-09541-6 Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar |
| url |
https://hdl.handle.net/20.500.12585/10338 https://doi.org/10.1007/s10883-021-09541-6 |
| dc.language.iso.spa.fl_str_mv |
eng |
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eng |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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Attribution-NonCommercial-NoDerivatives 4.0 Internacional |
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openAccess |
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application/pdf |
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27 páginas |
| dc.publisher.place.spa.fl_str_mv |
Cartagena de Indias |
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Springer Science+Business Media, LLC, part of Springer Nature 2021 |
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Universidad Tecnológica de Bolívar |
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Rodrigues, Fagner B.2bbd33e0-29cb-4a32-beef-a9715e693e83Muentes Acevedo, Jeovannya00a2fcf-ed20-430d-a46b-2195dd9675d52021-07-29T19:26:35Z2021-07-29T19:26:35Z2020-10-072021-07-29Rodrigues, F.B., Acevedo, J.M. Mean Dimension and Metric Mean Dimension for Non-autonomous Dynamical Systems. J Dyn Control Syst (2021). https://doi.org/10.1007/s10883-021-09541-6https://hdl.handle.net/20.500.12585/10338https://doi.org/10.1007/s10883-021-09541-6Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarIn this paper we extend the definitions of mean dimension and metric mean dimension for non-autonomous dynamical systems. We show some properties of this extension and furthermore some applications to the mean dimension and metric mean dimension of single continuous maps.application/pdf27 páginasenghttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://purl.org/coar/access_right/c_abf2Springer Science+Business Media, LLC, part of Springer Nature 2021Mean Dimension and Metric Mean Dimension for Non-autonomous Dynamical Systemsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/restrictedAccesshttp://purl.org/coar/resource_type/c_2df8fbb1Non-autonomous dynamical systemsMean dimensionMetric mean dimensionTopological entropyCartagena de IndiasInvestigadoresFreitas AC, Freitas JM, Vaienti S. Extreme value laws for non stationary processes generated by sequential and random dynamical systems. Annales de l’Institut Henri Poincaré, probabilités et statistiques; 2017. Institut Henri Poincaré.Gromov M. Topological invariants of dynamical systems and spaces of holomorphic maps: I. Math Phys Anal Geom 1999;2(4):323–415.Gutman Y, Tsukamoto M. 2015. Embedding minimal dynamical systems into Hilbert cubes. arXiv:1511.01802.Katok A, Hasselblatt B, Vol. 54. Introduction to the modern theory of dynamical systems. Cambridge: Cambridge University Press; 1995.Kawabata T, Dembo A. The rate-distortion dimension of sets and measures. IEEE Trans Inf Theory 1994;40(5):1564–72.Kloeckner B. Optimal transport and dynamics of expanding circle maps acting on measures. Ergodic Theory Dyn Syst 2013;33(2):529–48.Kolyada S, Snoha L. Topological entropy of nonautonomous dynamical systems. Random Comput Dyn 1996;4(2):205.Li H. Sofic mean dimension. Adv Math 2013;244:570–604.Lindenstrauss E. Mean dimension, small entropy factors and an embedding theorem. Publ Math Inst des Hautes Études Scientifiques 1999;89(1):227–262Lindenstrauss E, Weiss B. Mean topological dimension. Israel J Math 2000;115(1):1–24.Lindenstrauss E, Tsukamoto M. From rate distortion theory to metric mean dimension: variational principle. IEEE Trans Inf Theory 2018;64(5):3590–609.Lindenstrauss E, Tsukamoto M. Mean dimension and an embedding problem: an example. Israel J Math 2014;199(5–2):573–84.Misiurewicz M. Horseshoes for continuous mappings of an interval. Dynamical systems. Berlin: Springer; 2010. p. 125–35.Muentes J. On the continuity of the topological entropy of non-autonomous dynamical systems. Bull Braz Math Soc New Ser 2018;49(1):89–106.Stadlbauer M. Coupling methods for random topological Markov chains. Ergodic Theory Dyn Syst 2017;37(3):971–94.Velozo A, Velozo R. 2017. Rate distortion theory, metric mean dimension and measure theoretic entropy. arXiv:1707.05762.Yano K. A remark on the topological entropy of homeomorphisms. Invent Math 1980;59(3):215–220.Zhu Y, et al. Entropy of nonautonomous dynamical systems. 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