Predictability, entropy and information of infinite transformations

Details Predictability, entropy and information of infinite transformations Predictability, entropy and information of infinite transformations

2007-05-15

arxiv.org/abs/0705.2148v5

Fund. Math. 206 (2009), 1--21

Mathematics

Dynamical Systems

typos corrected, clarifications added, unproved result removed

Scientific paper

We show that a certain type of quasi finite, 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 quasi finite; and consider distribution asymptotics of information showing that e.g. for Boole's transformation, information is asymptotically mod-normal with square root normalization. Lastly we see that certain ergodic, probability preserving transformations with zero entropy have analogous properties and consequently entropy dimension of at most 1/2.

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