Summary
The 2018 International Symposium on Information Theory and Its Applications (ISITA2018)
2018
Session Number:We-PM-1-3
Session:
Number:We-PM-1-3.3
Invariant Measures for the Subshifts Associated with the Asymmetric Binary Systems
Hiroshi Fujisaki,
pp.675-679
Publication Date:2018/10/18
Online ISSN:2188-5079
DOI:10.34385/proc.55.We-PM-1-3.3
PDF download
Summary:
For a probability vector (p,1 - p), we assume that β = 1/p is a reduced quadratic irrational. Then, we show that the coding function for the asymmetric binary systems (ABS) determines a factor of the subshift arising from a substitution. For the case where β is the golden mean, we give an explicit formula of the probability of states in the ABS. Index Terms?ABS (asymmetric binary systems), substitution dynamical systems, continued fraction expansion, invariant measure