Relation between integer-valued Markov measures and measures with independent values

1988 ◽  
Vol 39 (6) ◽  
pp. 564-568
Author(s):  
E. B. Bakhovets
Keyword(s):  
Markov Measures

AN UPPER BOUND OF THE DIRECTIONAL ENTROPY WITH RESPECT TO THE MARKOV MEASURES

2012 ◽  
Vol 22 (11) ◽  
pp. 1250263 ◽  
Author(s):  
HASAN AKIN
Keyword(s):  
Upper Bound ◽  
Stochastic Matrix ◽  
Natural Extension ◽  
Short Paper ◽  
Probability Vector ◽  
Compact Metric Space ◽  
One Dimensional ◽  
Markov Measure ◽  
Shift Map ◽  
Markov Measures

In this short paper, without considering the natural extension we study the directional entropy of a Z2-action Φ generated by an invertible one-dimensional linear cellular automaton [Formula: see text] and [Formula: see text], over the ring Zpk(with p a prime number and k ≥ 2), where gcd (p, λr) = 1 and p ∣ λifor all i ≠ r, and the shift map acting on the compact metric space [Formula: see text]. Without loss of generality, we consider k = 2. We prove that the directional entropy hv(Φ)(v = (s, q) ∈ R) of a Z2-action with respect to a Markov measure μπPover space [Formula: see text] defined by a stochastic matrix P = (aij) and a probability vector π = {π0, π1, …, πp2-1} is bounded above by [Formula: see text].

scholarly journals The Measure-Theoretic Entropy and Topological Entropy of Actions overℤm

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Chih-Hung Chang ◽  
Yu-Wen Chen
Keyword(s):  
Invariant Measure ◽  
Cellular Automata ◽  
Topological Entropy ◽  
Finite Ring ◽  
One Dimensional ◽  
Maximal Measure ◽  
Bernoulli Measure ◽  
Markov Measures ◽  
Infinite Sequences

This paper studies the quantitative behavior of a class of one-dimensional cellular automata, named weakly permutive cellular automata, acting on the space of all doubly infinite sequences with values in a finite ringℤm,m≥2. We calculate the measure-theoretic entropy and the topological entropy of weakly permutive cellular automata with respect to any invariant measure on the spaceℤmℤ. As an application, it is shown that the uniform Bernoulli measure is the unique maximal measure for linear cellular automata among the Markov measures.

scholarly journals Product and Markov measures of type III

1998 ◽  
Vol 65 (1) ◽  
pp. 84-110 ◽  
Author(s):  
Anthony H. Dooley ◽  
Ivo Klemeš ◽  
Anthony N. Quas
Keyword(s):  
Type Iii ◽  
Explicit Constructions ◽  
Product Measures ◽  
Markov Measures

AbstractWe give some explicit constructions of type III product measures with various properties, resolving some conjectures of Brown, Dooley and Lake. We also define a family of Markov odometers of type III0 and show that the associated flow is approximately transitive.

scholarly journals Markov measures determine the zeta function

1987 ◽  
Vol 7 (2) ◽  
pp. 303-311 ◽  
Author(s):  
Selim Tuncel
Keyword(s):  
Zeta Function ◽  
Finite Type ◽  
Periodic Orbits ◽  
Point Of View ◽  
Subshifts Of Finite Type ◽  
Markov Measures ◽  
Markov Equivalence

AbstractWith the purpose of understanding when two subshifts of finite type are equivalent from the point of view of their spaces of Markov measures we propose the notion of Markov equivalence. We show that a Markov equivalence must respect the cycles (periodic orbits) of the subshifts. In particular, Markov equivalent subshifts of finite type have the same zeta function.

scholarly journals Infinite-to-one codes and Markov measures

1984 ◽  
Vol 285 (2) ◽  
pp. 657-657 ◽  
Author(s):  
Mike Boyle ◽  
Selim Tuncel
Keyword(s):  
Markov Measures
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