TOEPLITZ SEQUENCES OF INTERMEDIATE COMPLEXITY

Title & Authors
TOEPLITZ SEQUENCES OF INTERMEDIATE COMPLEXITY
Kim, Hyoung-Keun; Park, Seung-Seol;

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 $\small{\frac{1}{2}}$. The second construction provides the Toeplitz sequences which have various entropy dimensions.
Keywords
Toeplitz sequences;entropy dimensions;intermediate complexity;
Language
English
Cited by
1.
COLORINGS OF TREES WITH LINEAR, INTERMEDIATE AND EXPONENTIAL SUBBALL COMPLEXITY,;;

대한수학회지, 2015. vol.52. 6, pp.1123-1137
1.
COLORINGS OF TREES WITH LINEAR, INTERMEDIATE AND EXPONENTIAL SUBBALL COMPLEXITY, Journal of the Korean Mathematical Society, 2015, 52, 6, 1123
References
1.
Y. Ahn, D. Dou, and K. Park, Entropy dimension and variational principle, to appear in Studia Mathematica.

2.
J. Cassaigne, Constructing innite words of intermediate complexity, Developments in language theory, 173-184, Lecture Notes in Comput. Sci., 2450, Springer, Berlin, 2003.

3.
J. Cassaigne and J. Karhumaki, Toeplitz words, generalized periodicity and periodically iterated morphisms, European J. Combin. 18 (1997), no. 5, 497-510.

4.
D. G. Champernowne, The construction of decimals normal in the scale of ten, J. London Math. Soc. 8 (1933), 254-260.

5.
D. Dou, W. Huang, and K. Park, Entropy dimension of topological dynamical systems, to appear in Transactions of AMS.

6.
D. Dou and K. Park, Examples of entropy generating sequence, preprint.

7.
S. Ferenczi, Complexity of sequences and dynamical systems, Discrete Math. 206 (1999), no. 1-3, 145-154.

8.
S. Ferenczi and K. Park, Entropy dimensions and a class of constructive examples, Discrete Contin. Dyn. Syst. 17 (2007), no. 1, 133-141.

9.
K. Jacobs and M. Keane, 0 - 1-sequences of Toeplitz type, Z. Wahrsch. Verw. Gebiete 13 (1969), 123-131.

10.
N. G. Markley and M. E. Paul, Almost automorphic symbolic minimal sets without unique ergodicity, Israel J. Math. 34 (1979), no. 3, 259-272.

11.
S. Williams, Toeplitz minimal ows which are not uniquely ergodic, Z. Wahrsch. Verw. Gebiete 67 (1984), no. 1, 95-107.