On Sequence Entropy of Thue - Morse Shift

• Autorzy: Foryś M.
• Języki publikacji: EN

Abstrakty

EN

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 Cn2 log 3 for some constant C > 0. In the second part we prove that the sequence entropy of XM is achieved for the sequence τ (i) = 22i - 1.

Słowa kluczowe

EN

entropy; Thue-Morse sequence; sequence entropy; pattern; pattern complexity

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Schedae Informaticae
• Rocznik: 2013
• Tom: Vol. 22
• Strony: 19--25
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Foryś M.

• Institute of Computer Science, Jagiellonian University, Prof. Stanisława Łojasiewicza 6, 30-348 Kraków, Poland

Bibliografia

• [1] Maass A., Shao S.; Structure of Bounded Topological-Sequence-Entropy Minimal Systems, Journal of the London Mathematical Society 76 (3), 2007, pp. 702-718.
• [2] 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.
• [3] Kamae T.; Maximal Pattern Complexity as Topological Invariants, preprint, Tokyo University, Available via http://www14.plala.or.jp/kamae/invariants.pdf.
• [4] Restivo A., Salemi S.; Overlap Free Words on Two Symbols, Lecture Notes in Computer Science 192, Springer, New York 1985, pp. 198-206.
• [5] Morse M., Hedlund G.A.; Symbolic Dynamics, American Journal of Mathematics 60(4), 1938, pp. 815-866.