TY - JOUR
T1 - Isomorphic extensions and applications
AU - Downarowicz, Tomasz
AU - Glasner, Eli
N1 - Publisher Copyright:
© 2016 Juliusz Schauder Centre for Nonlinear Studies Nicolaus Copernicus University.
PY - 2016/9
Y1 - 2016/9
N2 - If π:(X,T)→(Z,S) is a topological factor map between uniquely ergodic topological dynamical systems, then (X,T) is called an isomorphic extension of (Z,S) if π is also a measure-theoretic isomorphism. We consider the case when the systems are minimal and we pay special attention to equicontinuous (Z,S). We first establish a characterization of this type of isomorphic extensions in terms of mean equicontinuity, and then show that an isomorphic extension need not be almost one-to-one, answering questions of Li, Tu and Ye.
AB - If π:(X,T)→(Z,S) is a topological factor map between uniquely ergodic topological dynamical systems, then (X,T) is called an isomorphic extension of (Z,S) if π is also a measure-theoretic isomorphism. We consider the case when the systems are minimal and we pay special attention to equicontinuous (Z,S). We first establish a characterization of this type of isomorphic extensions in terms of mean equicontinuity, and then show that an isomorphic extension need not be almost one-to-one, answering questions of Li, Tu and Ye.
KW - Almost oneto-one extension
KW - Isomorphic extension
KW - Mean equicontinuity
KW - Minimality
KW - Skew product
KW - Unique ergodicity
UR - http://www.scopus.com/inward/record.url?scp=84992084103&partnerID=8YFLogxK
U2 - 10.12775/TMNA.2016.050
DO - 10.12775/TMNA.2016.050
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AN - SCOPUS:84992084103
SN - 1230-3429
VL - 48
SP - 321
EP - 338
JO - Topological Methods in Nonlinear Analysis
JF - Topological Methods in Nonlinear Analysis
IS - 1
ER -