Odometer Based Systems

Matthew Foreman*, Benjamin Weiss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Construction sequences are a general method of building symbolic shifts that capture cut-and-stack constructions and are general enough to give symbolic representations of Anosov-Katok diffeomorphisms. We show here that any finite entropy system that has an odometer factor can be represented as the limit of a special class of construction sequences, the odometer based construction sequences. These naturally correspond to those cut-and-stack constructions that do not use spacers. The odometer based construction sequences can be constructed to have the small word property and every Choquet simplex can be realized as the simplex of invariant measures of the limit of an odometer based construction sequence.

Original languageEnglish
Pages (from-to)327-364
Number of pages38
JournalIsrael Journal of Mathematics
Volume251
Issue number1
DOIs
StatePublished - Dec 2022

Bibliographical note

Publisher Copyright:
© 2022, The Hebrew University of Jerusalem.

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