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TOEPLITZ SEQUENCES OF INTERMEDIATE COMPLEXITY

김형근|박승설
대한수학회 (The Korean Mathematical Society)|2011.03|대한수학회지 (Journal of the KMS)|제48권 제2호|pp. 383-395

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참고문헌

키워드

Toeplitz sequencesentropy dimensionsintermediate complexity
주제분류수학

초록

We present two constructions of Toeplitz sequences with an intermediate complexity function by using the generalized Oxtoby sequence. In the rst one, we use the blocks from the in nite sequence,which has entropy dimension ½ . The second construction provides the Toeplitz sequences which have various entropy dimensions.

Abstract

We present two constructions of Toeplitz sequences with an intermediate complexity function by using the generalized Oxtoby sequence. In the rst one, we use the blocks from the in nite sequence,which has entropy dimension ½ . The second construction provides the Toeplitz sequences which have various entropy dimensions.

참고문헌 (11)

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  4. D. G. Champernowne, "The construction of decimals normal in the scale of ten", J. London Math. Soc, 8, pp.254~260 (1933)
  5. D. Dou, "Entropy dimension of topological dynamical systems", to appear in Transactions of AMS, ~
  6. D. Dou, "Examples of entropy generating sequence"
  7. S. Ferenczi, "Complexity of sequences and dynamical systems", Discrete Math, 206(1), pp.145~154 (1999)
  8. S. Ferenczi, "Entropy dimensions and a class of constructive examples", Discrete Contin. Dyn. Syst, 17(1), pp.133~141 (2007)
  9. K. Jacobs, "0 - 1-sequences of Toeplitz type", Z. Wahrsch. Verw. Gebiete, 13, pp.123~131 (1969)
  10. N. G. Markley, "Almost automorphic symbolic minimal sets without unique ergodicity", Israel J. Math, 34(3), pp.259~272 (1979)
  11. S. Williams, "Toeplitz minimal ows which are not uniquely ergodic", Z. Wahrsch. Verw. Gebiete, 67(1), pp.95~107 (1984)

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