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/
| Summary: | 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). |
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