Hölder continuous maps on the interval with positive metric mean dimension

Author:

Muentes Acevedo Jeovanny de Jesus,Romaña Ibarra Sergio Augusto,Arias Cantillo Raibel de Jesus

Abstract

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 (H), 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.

Publisher

Universidad Nacional de Colombia

Reference9 articles.

1. J. Muentes Acevedo, Genericity of continuous maps with positive metric mean dimension, Results in Mathematics 77 (2022), no. 1, 2.

2. M. Carvalho, B. Fagner Rodrigues, and P. Varandas, Generic homeomorphisms have full metric mean dimension, Ergodic Theory and Dynamical Systems 42 (2022), no. 1, 40-64.

3. P. Hazard, Maps in dimension one with infinite entropy, Arkiv för Matematik 58 (2020), no. 1, 95-119.

4. A. Katok and B. Hasselblatt, Introduction to the modern theory of dynamical systems, vol. 54, Cambridge university press, 1997.

5. S. Kolyada and S. Lubomir, Topological entropy of nonautonomous dynamical systems, Random and computational dynamics 4 (1996), no. 2, 205.

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