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α-Equivalence

Kyewon Koh Park — 1998

Studia Mathematica

We define the α - relations between discrete systems and between continuous systems. We show that it is an equivalence relation. α- Equivalence vs. even α-equivalence is analogous to Kakutani equivalence vs. even Kakutani equivalence.

Predictability, entropy and information of infinite transformations

Jon AaronsonKyewon Koh Park — 2009

Fundamenta Mathematicae

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...

Topological disjointness from entropy zero systems

Wen HuangKyewon Koh ParkXiangdong Ye — 2007

Bulletin de la Société Mathématique de France

The properties of topological dynamical systems ( X , T ) which are disjoint from all minimal systems of zero entropy, 0 , are investigated. Unlike the measurable case, it is known that topological K -systems make up a proper subset of the systems which are disjoint from 0 . We show that ( X , T ) has an invariant measure with full support, and if in addition ( X , T ) is transitive, then ( X , T ) is weakly mixing. A transitive diagonal system with only one minimal point is constructed. As a consequence, there exists a thickly syndetic...

Entropy dimension and variational principle

Young-Ho AhnDou DouKyewon Koh Park — 2010

Studia Mathematica

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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