Set of periods of a subshift

Proceedings - Mathematical Sciences - Tập 128 - Trang 1-8 - 2018
K Ali Akbar1, V Kannan2
1Department of Mathematics, Central University of Kerala, Kasaragod, India
2School of Mathematics and Statistics, University of Hyderabad, Hyderabad, India

Tóm tắt

In this article, subsets of $${\mathbb {N}}$$ that can arise as sets of periods of the following subshifts are characterized: (i) subshifts of finite type, (ii) transitive subshifts of finite type, (iii) sofic shifts, (iv) transitive sofic shifts, and (v) arbitrary subshifts.

Tài liệu tham khảo

Ali Akbar K, Some Results in Linear, Symbolic and General Topological Dynamics, PhD thesis (2010) (University of Hyderabad) Ali Akbar K, Periods of endomorphisms on an abelian group, Topology Proceedings (2013) vol. 42, pp. 341–347 Ali Akbar K, Kannan V, Gopal Sharan and Chiranjeevi P, The set of periods of periodic points of a linear operator, Linear Algebra Appl., 431 (2009) 241–246 Apostol Tom M, Introduction to Analytic Number Theory, Springer International Student Edition (1989) (New Delhi, India: Narosa Publishing House) Baker I N, Fix-points of polynomials and rational functions, J. London Math. Soc., 39 (1964) 615–622 Block L S and Coppel W A, Dynamics in One Dimension, volume 1513 of Lecture Notes in Mathematics (1992) (Berlin: Springer-Verlag) Brin M and Stuck G, Introduction to Dynamical Systems (2002) (Cambridge University Press) Devaney R L, An Introduction to Chaotic Dynamical Systems, second edition (1989) (Redwood City, CA: Addison-Wesley Publishing Company Advanced Book Program) Kannan V, Subramania Pillai I, Ali Akbar K and Sankararao B, The set of periods of periodic points of a toral automorphism, Topology Proceedings (2011) Kurka P, Topological and Symbolic Dynamics (Prague, Czech Republic: Charles University) Lind D A and Marcus B, An introduction to symbolic dynamics and coding (1995) (New York, USA: Cambridge University Press) Sai Sesha, Ph.D. thesis, Symbolic Dynamics for Complete Classification (2000) (University of Hyderabad) Subrahmonian Moothathu T K, Set of periods of additive cellular automata, Theor. Computer Sci., 352 (2006) 226–331