TY - JOUR
T1 - The critical dimension for G-measures
AU - Mansfield, Daniel F.
AU - Dooley, Anthony H.
PY - 2017/5
Y1 - 2017/5
N2 - The critical dimension of an ergodic non-singular dynamical system is the asymptotic growth rate of sums of consecutive Radon–Nikodým derivatives. This has been shown to equal the average coordinate entropy for product odometers when the size of individual factors is bounded. We extend this result to (Formula presented.)-measures with an asymptotic bound on the size of individual factors. Furthermore, unlike von Neumann–Krieger type, the critical dimension is an invariant property on the class of ergodic (Formula presented.)-measures.
AB - The critical dimension of an ergodic non-singular dynamical system is the asymptotic growth rate of sums of consecutive Radon–Nikodým derivatives. This has been shown to equal the average coordinate entropy for product odometers when the size of individual factors is bounded. We extend this result to (Formula presented.)-measures with an asymptotic bound on the size of individual factors. Furthermore, unlike von Neumann–Krieger type, the critical dimension is an invariant property on the class of ergodic (Formula presented.)-measures.
UR - http://www.scopus.com/inward/record.url?scp=84944936991&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1017/etds.2015.69
U2 - 10.1017/etds.2015.69
DO - 10.1017/etds.2015.69
M3 - Article
AN - SCOPUS:84944936991
SN - 0143-3857
VL - 37
SP - 824
EP - 836
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 3
ER -