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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.
Young-Ho Ahn, Dou Dou, and Kyewon Koh Park. "Entropy dimension and variational principle." Studia Mathematica 199.3 (2010): 295-309. <http://eudml.org/doc/285733>.
@article{Young2010, 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.}, author = {Young-Ho Ahn, Dou Dou, Kyewon Koh Park}, journal = {Studia Mathematica}, keywords = {entropy dimension; variational principle; zero entropy system}, language = {eng}, number = {3}, pages = {295-309}, title = {Entropy dimension and variational principle}, url = {http://eudml.org/doc/285733}, volume = {199}, year = {2010}, }
TY - JOUR AU - Young-Ho Ahn AU - Dou Dou AU - Kyewon Koh Park TI - Entropy dimension and variational principle JO - Studia Mathematica PY - 2010 VL - 199 IS - 3 SP - 295 EP - 309 AB - 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. LA - eng KW - entropy dimension; variational principle; zero entropy system UR - http://eudml.org/doc/285733 ER -