Predictability, entropy and information of infinite transformations

Jon Aaronson*, Kyewon Koh Park

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 α √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.

Original languageEnglish
Pages (from-to)1-21
Number of pages21
JournalFundamenta Mathematicae
Volume206
Issue number1
DOIs
StatePublished - 2009

Keywords

  • Conservative
  • Entropy
  • Entropy dimension
  • Ergodic
  • Measure preserving transformation
  • Predictable set
  • Quasifinite

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