On Sequence Entropy of Thue-Morse Shift
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RIS BIB ENDNOTEOn Sequence Entropy of Thue-Morse Shift
Publication date: 06.06.2014
Schedae Informaticae, 2013, Volume 22, pp. 19-25
https://doi.org/10.4467/20838476SI.13.002.2087Authors
On Sequence Entropy of Thue-Morse Shift
The paper summarizes properties of topological and sequence en- tropy of the Morse shift XM generated by the Thue-Morse sequence tM. The first part is an estimation of growth rate of possible subwords in tM. We show a polynomial upper bound on the number of finite subwords occuring in tM which is Cn2log3 for some constant C > 0. In the second part we prove that the sequence entropy of XM is achieved for the sequence r(i) = 22i − 1.
Maass A., Shao S.; Structure of Bounded Topological-Sequence-Entropy Minimal Sys- tems, Journal of the London Mathematical Society 76 (3), 2007, pp. 702–718.
Kamae T., Zamboni L.; Sequence Entropy and the Maximal Pattern Complexity of Infinite Words, Ergodic Theory and Dynamical Systems 22 (4), 2002, pp. 1191–1199.
Kamae T.; Maximal Pattern Complexity as Topological Invariants, preprint, Tokyo University, Available via http://www14.plala.or.jp/kamae/invariants.pdf.
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Morse M., Hedlund G.A.; Symbolic Dynamics, American Journal of Mathematics 60(4), 1938, pp. 815–866.
Information: Schedae Informaticae, 2013, Volume 22, pp. 19-25
Article type: Original scientific article
Institute of Computer Science, Jagiellonian University, Poland
Published at: 06.06.2014
Article status: Open
Licence: None
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