Recently the notions of entropy dimension for topological and measurable dynamical systems were introduced in order to study the complexity of zero entropy systems. We exhibit a class of strictly ergodic models whose topological entropy dimensions range from zero to one and whose measure-theoretic entropy dimensions are identically zero. Hence entropy dimension does not obey the variational principle.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-3-6,
author = {Young-Ho Ahn and Dou Dou and Kyewon Koh Park},
title = {Entropy dimension and variational principle},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {295-309},
zbl = {1215.37013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-3-6}
}
Young-Ho Ahn; Dou Dou; Kyewon Koh Park. Entropy dimension and variational principle. Studia Mathematica, Tome 196 (2010) pp. 295-309. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-3-6/