{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T13:06:42Z","timestamp":1762952802314,"version":"3.45.0"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Fractal Geom."],"accepted":{"date-parts":[[2025,5,21]]},"published-print":{"date-parts":[[2025,7,16]]},"abstract":"<jats:p>Metric mean dimension is a geometric invariant of dynamical systems with infinite topological entropy. We relate this concept with the fractal structure of the phase space and the H\u00f6lder regularity of the map. Afterwards, we improve our general estimates in a family of interval maps by computing the metric mean dimension in a way similar to the Misiurewicz formula for the entropy, which in particular shows that our bounds are sharp. As an application, we determine the metric mean dimension of the classical Weierstrass functions. Of independent interest, we develop a dynamical analogue of the Minkowski\u2013Bouligand dimension for subshifts on Ahlfors regular alphabets, which also provides an entropy formula in terms of the size of the set of admissible words, generalizing the classical result for subshifts on finite alphabets.<\/jats:p>","DOI":"10.4171\/jfg\/169","type":"journal-article","created":{"date-parts":[[2025,7,16]],"date-time":"2025-07-16T09:49:17Z","timestamp":1752659357000},"source":"Crossref","is-referenced-by-count":0,"title":["Metric mean dimension, H\u00f6lder regularity and Assouad spectrum"],"prefix":"10.4171","author":[{"given":"Alexandre","family":"Baraviera","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/041yk2d64","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6929-6442","authenticated-orcid":false,"given":"Maria","family":"Carvalho","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/043pwc612","id-type":"ROR","asserted-by":"publisher"}],"name":"Faculdade de Ci\u00eancias da Universidade do Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3789-256X","authenticated-orcid":false,"given":"Gustavo","family":"Pessil","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/043pwc612","id-type":"ROR","asserted-by":"publisher"}],"name":"Faculdade de Ci\u00eancias da Universidade do Porto, Portugal"}]}],"member":"2673","container-title":["Journal of Fractal Geometry, Mathematics of Fractals and Related Topics"],"original-title":[],"deposited":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T13:01:37Z","timestamp":1762952497000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/jfg\/169"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,16]]},"references-count":0,"URL":"https:\/\/doi.org\/10.4171\/jfg\/169","relation":{},"ISSN":["2308-1309","2308-1317"],"issn-type":[{"type":"print","value":"2308-1309"},{"type":"electronic","value":"2308-1317"}],"subject":[],"published":{"date-parts":[[2025,7,16]]}}}