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Entropy pairs of ℤ² and their directional properties

100%
Park K., Lee U.
Studia Mathematica
|
2004
|
tom 165
|
nr 3
255-274
EN
Topological and metric entropy pairs of ℤ²-actions are defined and their properties are investigated, analogously to ℤ-actions. In particular, mixing properties are studied in connection with entropy pairs.
2
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Predictability, entropy and information of infinite transformations

100%
Aaronson J., Park K.
Fundamenta Mathematicae
|
2009
|
tom 206
|
nr 1
1-21
EN
We show that a certain type of quasifinite, conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic, measure preserving transformation which is not quasifinite; and consider distribution asymptotics of information showing that e.g. for Boole's transformation, information is asymptotically mod-normal with normalization ∝ √n. Lastly, we show that certain ergodic, probability preserving transformations with zero entropy have analogous properties and consequently entropy dimension of at most 1/2.
3
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Entropy dimension and variational principle

81%
Ahn Y.-H., Dou D., Park K.
Studia Mathematica
|
2010
|
tom 199
|
nr 3
295-309
EN
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.
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