INSTYTUT MATEMATYCZNY · POLSKA AKADEMIA NAUK STUDIA MATHEMATICA ISSN: 0039-3223(p) 1730-6337(e)

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Entropy dimension and variational principle

Young-Ho Ahn¹, Dou Dou², Kyewon Koh Park³
Studia Math. 199 (2010), 295-309
doi:10.4064/sm199-3-6
Abstract: 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.

MSC (2010): Primary 37A35; Secondary 37A25.
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1. Department of Mathematics
   Mokpo National University
   534-729 Mokpo, South Korea
   
2. Department of Mathematics
   Nanjing University
   210093 Nanjing, P.R. China
   
3. Department of Mathematics
   Ajou University
   442-749 Suwon, South Korea
   

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