TY - JOUR
T1 - Substitution-dynamics and invariant measures for infinite alphabet-path space
AU - Bezuglyi, Sergey
AU - Jorgensen, Palle E.T.
AU - Sanadhya, Shrey
N1 - Publisher Copyright:
© 2024 Elsevier Inc.
PY - 2024/5/1
Y1 - 2024/5/1
N2 - We study substitutions on a countably infinite alphabet (without compactification) as Borel dynamical systems. We construct stationary and non-stationary generalized Bratteli-Vershik models for a class of such substitutions, known as left determined. In this setting of Borel dynamics, using a stationary generalized Bratteli-Vershik model, we provide a new and canonical construction of shift-invariant measures (both finite and infinite) for the associated class of subshifts.
AB - We study substitutions on a countably infinite alphabet (without compactification) as Borel dynamical systems. We construct stationary and non-stationary generalized Bratteli-Vershik models for a class of such substitutions, known as left determined. In this setting of Borel dynamics, using a stationary generalized Bratteli-Vershik model, we provide a new and canonical construction of shift-invariant measures (both finite and infinite) for the associated class of subshifts.
KW - Borel dynamical systems
KW - Bratteli-Vershik model
KW - Infinite alphabet
KW - Shift-invariant measures
KW - Substitutions
KW - Tail invariant measures
UR - http://www.scopus.com/inward/record.url?scp=85187237938&partnerID=8YFLogxK
U2 - 10.1016/j.aam.2024.102687
DO - 10.1016/j.aam.2024.102687
M3 - Article
AN - SCOPUS:85187237938
SN - 0196-8858
VL - 156
JO - Advances in Applied Mathematics
JF - Advances in Applied Mathematics
M1 - 102687
ER -