Balanced Shifts
DOI:
https://doi.org/10.26713/cma.v11i3.883Keywords:
Synchronized systems, Half synchronized, Dyke systems, Balanced block, EntropyAbstract
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.
Downloads
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.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.