TY - JOUR
T1 - On the critical dimensions of product odometers
AU - Dooley, Anthony H.
AU - Mortiss, Genevieve
PY - 2009/4/1
Y1 - 2009/4/1
N2 - Mortiss introduced the notion of critical dimension of a non-singular action, a measure of the order of growth of sums of Radon derivatives. The critical dimension was shown to be an invariant of metric isomorphism; this invariant was calculated for two-point product odometers and shown to coincide, in certain cases, with the average coordinate entropy. In this paper we extend the theory to apply to all product odometers, introduce upper and lower critical dimensions, and prove a Katok-type covering lemma.
AB - Mortiss introduced the notion of critical dimension of a non-singular action, a measure of the order of growth of sums of Radon derivatives. The critical dimension was shown to be an invariant of metric isomorphism; this invariant was calculated for two-point product odometers and shown to coincide, in certain cases, with the average coordinate entropy. In this paper we extend the theory to apply to all product odometers, introduce upper and lower critical dimensions, and prove a Katok-type covering lemma.
UR - http://www.scopus.com/inward/record.url?scp=69849085472&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1017/S0143385708000606
U2 - 10.1017/S0143385708000606
DO - 10.1017/S0143385708000606
M3 - Article
SN - 0143-3857
VL - 29
SP - 475
EP - 485
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 02
ER -