Browse > Article
http://dx.doi.org/10.4134/JKMS.2005.42.4.857

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

AHN YOUNG-HO (Department of Mathematics Mokpo National University)
LEE JUNGSEOB (Department of Mathematics Ajou University)
PARK KYEWON KOH (Department of Mathematics Ajou University)
Publication Information
Journal of the Korean Mathematical Society / v.42, no.4, 2005 , pp. 857-869 More about this Journal
Abstract
Let $(X,\;B,\;{\mu},\;T)$ 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 ${\mu}-Kronecker$ 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;
Citations & Related Records

Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
연도 인용수 순위
1 F. Blanchard, E. Glasner, and E. Host, A variation on the variational principle and applications to entropy pairs, Ergodic Theory Dynam. Systems 17 (1997), 29-43   DOI   ScienceOn
2 F. Blanchard and Y. Lacroix, Zero entropy factors of topological flows, Proc. Amer. Math. Soc. 119 (1993), no. 2, 985-992
3 E. Glasner, Ergodic theory via joinings, Math. Surverys Monogr. 101 (2003)
4 T. Goodman Topological sequence entropy, Proc. London Math. Soc. 29 (1974), no. 3, 331-350
5 W. Huang, S. Li, S. Shao, and X. Ye, Null systems and sequence entropy pairs, Ergodic Theory Dynam. Systems 23 (2003), no. 3, 1505-1523   DOI   ScienceOn
6 M. Lemanczyk and A. Siemaszko, A note on the existence of a largest topological factors with zero entropy, Proc. Amer. Math. Soc. 129 (2001), 475-485   DOI   ScienceOn
7 K. K. Park and A. Siemaszko, Relative topological Pinsker factors and entropy pairs, Monatsh. Math. 134 (2001), 67-79   DOI   ScienceOn
8 E. Glasner, A simple characterization of the set of $\mu$-entropy pairs and applica- tion, Israel J. Math. 102 (1997), 13-27   DOI
9 P. Hulse, Sequence entropy relative to an invariant $\sigma$-algebra, J. London Math Soc. 33 (1986), no. 2, 59-72   DOI
10 W. Huang, A. Maass, and X. Ye, Sequence entropy pairs for a measure, Ann. Inst. Fourier, to appear