[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2011.48.2.383

TOEPLITZ SEQUENCES OF INTERMEDIATE COMPLEXITY

Kim, Hyoung-Keun (DEPARTMENT OF MATHEMATICS AJOU UNIVERSITY)
Park, Seung-Seol (DEPARTMENT OF MATHEMATICS AJOU UNIVERSITY)

Publication Information

Journal of the Korean Mathematical Society / v.48, no.2, 2011 , pp. 383-395 More about this Journal

Abstract

We present two constructions of Toeplitz sequences with an intermediate complexity function by using the generalized Oxtoby sequence. In the first one, we use the blocks from the infinite sequence, which has entropy dimension $\frac{1}{2}$ . The second construction provides the Toeplitz sequences which have various entropy dimensions.

Keywords

Toeplitz sequences; entropy dimensions; intermediate complexity;

Citations & Related Records

Times Cited By Web Of Science : 0 (Related Records In Web of Science)
Times Cited By SCOPUS : 0

Reference

1	J. Cassaigne, Constructing innite words of intermediate complexity, Developments in language theory, 173-184, Lecture Notes in Comput. Sci., 2450, Springer, Berlin, 2003. DOI ScienceOn
2	J. Cassaigne and J. Karhumaki, Toeplitz words, generalized periodicity and periodically iterated morphisms, European J. Combin. 18 (1997), no. 5, 497-510. DOI ScienceOn
3	D. G. Champernowne, The construction of decimals normal in the scale of ten, J. London Math. Soc. 8 (1933), 254-260. DOI
4	D. Dou, W. Huang, and K. Park, Entropy dimension of topological dynamical systems, to appear in Transactions of AMS.
5	D. Dou and K. Park, Examples of entropy generating sequence, preprint.
6	S. Ferenczi, Complexity of sequences and dynamical systems, Discrete Math. 206 (1999), no. 1-3, 145-154. DOI ScienceOn
7	S. Ferenczi and K. Park, Entropy dimensions and a class of constructive examples, Discrete Contin. Dyn. Syst. 17 (2007), no. 1, 133-141. DOI
8	K. Jacobs and M. Keane, 0 - 1-sequences of Toeplitz type, Z. Wahrsch. Verw. Gebiete 13 (1969), 123-131. DOI
9	N. G. Markley and M. E. Paul, Almost automorphic symbolic minimal sets without unique ergodicity, Israel J. Math. 34 (1979), no. 3, 259-272. DOI
10	S. Williams, Toeplitz minimal ows which are not uniquely ergodic, Z. Wahrsch. Verw. Gebiete 67 (1984), no. 1, 95-107. DOI
11	Y. Ahn, D. Dou, and K. Park, Entropy dimension and variational principle, to appear in Studia Mathematica.