markov measures
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Author(s):  
Daniel Alpay ◽  
Palle Jorgensen ◽  
Izchak Lewkowicz


2016 ◽  
Vol 17 (01) ◽  
pp. 1750006
Author(s):  
Katsukuni Nakagawa

We give an answer to the multifractal rigidity problem presented by Barreira, Pesin and Schmeling for the dimension spectra of Markov measures on the repellers of piecewise linear Markov maps with two branches. Thermodynamic formalism provides us with a one-parameter family of measures. Zero-temperature limit measures of this family and the concept of nondegeneracy of spectra play important roles.



2016 ◽  
Vol 46 (2) ◽  
pp. 169-182
Author(s):  
Chun WEI ◽  
Hui LI ◽  
ShengYou WEN


2016 ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Ahmad Fadillah Embong
Keyword(s):  


2014 ◽  
Vol 267 (4) ◽  
pp. 1011-1034 ◽  
Author(s):  
Dorin Ervin Dutkay ◽  
Palle E.T. Jorgensen


2014 ◽  
Vol 35 (7) ◽  
pp. 2080-2093 ◽  
Author(s):  
DORIN ERVIN DUTKAY ◽  
PALLE E. T. JORGENSEN

In this paper, we answer the question of equivalence, or singularity, of two given quasi-stationary Markov measures on one-sided infinite words, as well as the corresponding question of equivalence of associated Cuntz algebra${\mathcal{O}}_{N}$-representations. We do this by associating certain monic representations of${\mathcal{O}}_{N}$to quasi-stationary Markov measures and then proving that equivalence for a pair of measures is decided by unitary equivalence of the corresponding pair of representations.



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.



2012 ◽  
Vol 22 (11) ◽  
pp. 1250263 ◽  
Author(s):  
HASAN AKIN

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].



2011 ◽  
Vol 176 (2) ◽  
pp. 255-269 ◽  
Author(s):  
E. A. Timofeev


2011 ◽  
Vol 38 (1-2) ◽  
pp. 305-323 ◽  
Author(s):  
P. E. T. Jorgensen ◽  
A. M. Paolucci


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