TY - JOUR
T1 - Odometer Based Systems
AU - Foreman, Matthew
AU - Weiss, Benjamin
N1 - Publisher Copyright:
© 2022, The Hebrew University of Jerusalem.
PY - 2022/12
Y1 - 2022/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85149521163&partnerID=8YFLogxK
U2 - 10.1007/s11856-022-2439-7
DO - 10.1007/s11856-022-2439-7
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85149521163
SN - 0021-2172
VL - 251
SP - 327
EP - 364
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -