TY - JOUR
T1 - Families of type III0 ergodic transformations in distinct orbit equivalent classes
AU - Dooley, A. H.
AU - Hawkins, J.
AU - Ralston, D.
PY - 2011/12/1
Y1 - 2011/12/1
N2 - A new isomorphism invariant of certain measure preserving flows, using sequences of integers, is introduced. Using this invariant, we are able to construct large families of type III0 systems which are not orbit equivalent. In particular we construct an uncountable family of nonsingular ergodic transformations, each having an associated flow that is approximately transitive (and therefore of zero entropy), with the property that the transformations are pairwise not orbit equivalent.
AB - A new isomorphism invariant of certain measure preserving flows, using sequences of integers, is introduced. Using this invariant, we are able to construct large families of type III0 systems which are not orbit equivalent. In particular we construct an uncountable family of nonsingular ergodic transformations, each having an associated flow that is approximately transitive (and therefore of zero entropy), with the property that the transformations are pairwise not orbit equivalent.
UR - http://www.scopus.com/inward/record.url?scp=81755166868&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1007/s00605-010-0258-0
U2 - 10.1007/s00605-010-0258-0
DO - 10.1007/s00605-010-0258-0
M3 - Article
SN - 0026-9255
VL - 164
SP - 369
EP - 381
JO - Monatshefte fur Mathematik
JF - Monatshefte fur Mathematik
IS - 4
ER -