Predictability, entropy and information of infinite transformations

Volume 206 / 2009

Jon Aaronson, Kyewon Koh Park Fundamenta Mathematicae 206 (2009), 1-21 MSC: 37A40, 60F05. DOI: 10.4064/fm206-0-1

Abstract

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 $\propto\sqrt n$. Lastly, we show that certain ergodic, probability preserving transformations with zero entropy have analogous properties and consequently entropy dimension of at most $1/2$.

Authors

  • Jon AaronsonSchool of Math. Sciences
    Tel Aviv University
    69978 Tel Aviv, Israel
    e-mail
  • Kyewon Koh ParkDepartment of Mathematics
    Ajou University
    Suwon 442-729, South Korea
    e-mail

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