Balanced Shifts

Authors

  • Dawoud Ahmadi Dastjerdi Department of Mathematics, Faculty of Mathematics, University of Guilan, Rasht, Guilan
  • M. Shahamat Department of Mathematics, Faculty of Mathematics, University of Guilan, Rasht, Guilan

DOI:

https://doi.org/10.26713/cma.v11i3.883

Keywords:

Synchronized systems, Half synchronized, Dyke systems, Balanced block, Entropy

Abstract

The notion of the balanced generator of the Dyke system (or Dyck system) has been extended to a general subshift called balanced shift and it has been shown that they are essentially mixing. All balanced shifts are half synchronized and full shifts are the only balanced and synchronized subshifts. Also, a formula for the Gurevic entropy of a balanced shift has been given.

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References

F. Blanchard and G. Hansel, Systèmes codès, Comp. Sci. 44 (1986), 17 – 49, https://core.ac.uk/download/pdf/82544327.pdf.

D. Fiebig and U. Fiebig, Covers for coded systems, Contemporary Mathematics 135 (1992), 139 – 179, https://books.google.co.in/books?hl=en&lr=&id=MlocCAAAQBAJ&oi=fnd&pg=PA139&dq=D.+Fiebig+and+U.+Fiebig,+Covers+for+coded+systems,+Contemporary+Mathematics,+135,+1992,+139-179.&ots=Yr-yyyHNIn&sig=Sab4O2uISjYkrlrbty3OXtf38EA#v=onepage&q&f=false.

U. Jung, On the existence of open and bi-continuous codes, Trans. Amer. Math. Soc. 363 (2011), 1399 – 1417, https://www.ams.org/journals/tran/2011-363-03/S0002-9947-2010-05035-4/S0002-9947-2010-05035-4.pdf.

K. Johnson, Beta-Shift Dynamical Systems and Their Associated Languages, PhD Thesis, The University of North Carolina at Chapel Hill (1999), http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.14.5020.

D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press (1995), DOI: 10.1017/CBO9780511626302.

T. Meyerovitch, Tail Invariant Measures of the Dyke-Shift and Non-Sofic Systems, MSc Thesis, Tel-Aviv University (2004), http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.137.4750&rep=rep1&type=pdf.

K. Thomsen, On the ergodic theory of synchronized systems, Ergod. Th. Dynam. Sys. 356 (2006), 1235 – 1256, https://pure.au.dk/portal/en/publications/on-the-ergodic-theory-of-synchronized-systems(466ae080-231f-11dc-bee9-02004c4f4f50).html.

K. Thomsen, On the structure of a sofic shift space, American Mathematical Society 356(9) , 3557 – 3619, https://www.jstor.org/stable/3844990.

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Published

30-09-2020
CITATION

How to Cite

Ahmadi Dastjerdi, D., & Shahamat, M. (2020). Balanced Shifts. Communications in Mathematics and Applications, 11(3), 415–424. https://doi.org/10.26713/cma.v11i3.883

Issue

Section

Research Article