Remarks on the entropy of sofic dynamical system of Blackwell's type

Autor: Z. I. Bezhaeva, V. I. Oseledets
Rok vydání: 2013
Předmět:
Zdroj: Journal of Dynamical and Control Systems. 19:301-308
ISSN: 1573-8698
1079-2724
DOI: 10.1007/s10883-013-9174-7
Popis: Consider a sofic dynamical system (X, T, μ), where X =A Z is the full symbolic compact set with the product topology, and A = {0, 1, . . . , d}. The shift is $$ T:\left\{ {{x_n}} \right\}\to \left\{ {{{{x^{\prime}}}_n}} \right\},{{x^{\prime}}_n}={x_n}+1 $$ . The measure μ is a T-invariant sofic probability measure. For all words a 1 . . . a n the measure is μ(a 1 . . . a n ) = μ({x : x 1 = a 1, . . . , x n = a n }) = $$ l{m_{{{a_1}}}}\ldots {m_{{{a_n}}}}r $$ . Matrices {m 0, . . . , m d }, d ? 1, are nonzero substochastic matrices of order J. The matrix P = m 0 +. . . + m d is a stochastic matrix, the row l is a left P-invariant probability row and all entries of the column r are equal to 1. We obtain an explicit formula for the entropy h(T, μ) of sofic dynamical system of Blackwell's type for which rank(m a ) = 1, a ? 0.
Databáze: OpenAIRE
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