Density of the level sets of the metric mean dimension for homeomorphisms
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Date
2023-12-10
Authors
Muentes Acevedo, Jeovanny de Jesus
Romaña Ibarra, Sergio
Arias Cantillo, Raibel
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Abstract
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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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