TY - JOUR
T1 - Computing the critical dimensions of Bratteli–Vershik systems with multiple edges
AU - Dooley, Anthony H.
AU - Hagihara, Rika
PY - 2012/2
Y1 - 2012/2
N2 - The critical dimension is an invariant that measures the growth rate of the sums of Radon–Nikodym derivatives for non-singular dynamical systems. We show that for Bratteli–Vershik systems with multiple edges, the critical dimension can be computed by a formula analogous to the Shannon–McMillan–Breiman theorem. This extends earlier results of Dooley and Mortiss on computing the critical dimensions for product and Markov odometers on infinite product spaces.
AB - The critical dimension is an invariant that measures the growth rate of the sums of Radon–Nikodym derivatives for non-singular dynamical systems. We show that for Bratteli–Vershik systems with multiple edges, the critical dimension can be computed by a formula analogous to the Shannon–McMillan–Breiman theorem. This extends earlier results of Dooley and Mortiss on computing the critical dimensions for product and Markov odometers on infinite product spaces.
UR - http://www.scopus.com/inward/record.url?scp=84655176500&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1017/S0143385710000969
U2 - 10.1017/S0143385710000969
DO - 10.1017/S0143385710000969
M3 - Article
SN - 0143-3857
VL - 32
SP - 103
EP - 117
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 01
ER -