RELATIVE SEQUENCE ENTROPY PAIRS FOR A MEASURE AND RELATIVE TOPOLOGICAL KRONECKER FACTOR

Title & Authors
RELATIVE SEQUENCE ENTROPY PAIRS FOR A MEASURE AND RELATIVE TOPOLOGICAL KRONECKER FACTOR
AHN YOUNG-HO; LEE JUNGSEOB; PARK KYEWON KOH;

Abstract
Let $\small{(X,\;B,\;{\mu},\;T)}$ be a dynamical system and (Y, A, v, S) be a factor. We investigate the relative sequence entropy of a partition of X via the maximal compact extension of (Y, A, v, S). We define relative sequence entropy pairs and using them, we find the relative topological $\small{{\mu}-Kronecker}$ factor over (Y, v) which is the maximal topological factor having relative discrete spectrum over (Y, v). We also describe the topological Kronecker factor which is the maximal factor having discrete spectrum for any invariant measure.
Keywords
relative sequence entropy;relative sequence entropy pairs;relative weakly mixing;compact extension;relative Kronecker factor;equicontinuous factor;null factor;
Language
English
Cited by
1.
Relativization of dynamical properties, Science China Mathematics, 2012, 55, 5, 913
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