Year: 2025
Type: article
Abstract: We investigate the metric mean dimension of subshifts of compact type. We prove that the metric mean dimensions of a continuous map and its inverse limit coincide, generalizing Bowen’s entropy formula. Building upon this result, we extend the notion of metric mean dimension to discontinuous maps in terms of suitable subshifts. As an application, we show that the metric mean dimension of the Gauss map and that of induced maps of the Manneville–Pomeau family is equal to the box dimension of the corresponding set of discontinuity points, which also coincides with a critical parameter of the pressure operator associated to the geometric potential.
Source: Nonlinearity
Author: Gustavo Pessil
Institutions: Universidade do Porto, Centro de Matemática
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,325
OpenAlex ID: W4408649722