maximal measure
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2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Chih-Hung Chang ◽  
Yu-Wen Chen

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.


2002 ◽  
Vol 127 (1) ◽  
pp. 253-277 ◽  
Author(s):  
Sylvie Ruette
Keyword(s):  

1997 ◽  
Vol 17 (6) ◽  
pp. 1419-1436 ◽  
Author(s):  
PETER RAITH

Let $T:X\to{\Bbb R}$ be a piecewise monotonic map, where $X$ is a finite union of closed intervals. Define $R(T)=\bigcap_{n=0}^{\infty} \overline{T^{-n}X}$, and suppose that $(R(T),T)$ has a unique maximal measure $\mu$. The influence of small perturbations of $T$ on the maximal measure is investigated. If $(R(T),T)$ has positive topological entropy, and if a certain stability condition is satisfied, then every piecewise monotonic map $\tilde{T}$, which is contained in a sufficiently small neighbourhood of $T$, has a unique maximal measure $\tilde{\mu}$, and the map $\tilde{T}\mapsto\tilde{\mu}$ is continuous at $T$.


1989 ◽  
Vol 20 (5) ◽  
pp. 1243-1254 ◽  
Author(s):  
Artur O. Lopes

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