Predictability, entropy and information of infinite transformations
Dynamical Systems
2010-06-01 v5 Probability
Abstract
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.
Cite
@article{arxiv.0705.2148,
title = {Predictability, entropy and information of infinite transformations},
author = {Jon Aaronson and Kyewon Koh Park},
journal= {arXiv preprint arXiv:0705.2148},
year = {2010}
}