?-Shifts have unique maximal measure

1978 ◽  
Vol 85 (3) ◽  
pp. 189-198 ◽  
Author(s):  
Franz Hofbauer
Keyword(s):  
Maximal Measure

The Dimension Spectrum of the Maximal Measure

1989 ◽  
Vol 20 (5) ◽  
pp. 1243-1254 ◽  
Author(s):  
Artur O. Lopes
Keyword(s):  
Dimension Spectrum ◽  
Maximal Measure

Stability of the maximal measure for piecewise monotonic interval maps

1997 ◽  
Vol 17 (6) ◽  
pp. 1419-1436 ◽  
Author(s):  
PETER RAITH
Keyword(s):  
Topological Entropy ◽  
Stability Condition ◽  
Finite Union ◽  
Small Perturbations ◽  
Interval Maps ◽  
Positive Topological Entropy ◽  
Maximal Measure ◽  
Closed Intervals ◽  
Piecewise Monotonic

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 $T$.

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 Points génériques de Champernowne sur certains systèmes codes; application aux θ-shifts

1988 ◽  
Vol 8 (1) ◽  
pp. 35-51 ◽  
Author(s):  
Anne Bertrand-Mathis
Keyword(s):  
Dynamical System ◽  
Invariant Measure ◽  
Nous Obtenons ◽  
Maximal Measure ◽  
Système Dynamique ◽  
Nous Montrons

AbstractWe show that if messages of length one, two, three…of a code X which verifies ρx* < ρx are concatenated, we obtain a point generic for an invariant measure on the dynamical system associated to the code; this measure is induced by the maximal measure on the tower studied by Hansel and Blanchard.Résumé. Nous montrons que si nous alignons les messages de longueur 1, puis 2, et ainsi de suite, d'un code X vérifiant ρx* < ρx, nous obtenons un point générique pour une mesure invariante sur le système dynamique associé au code en question; nous montrons que cette mesure se trouve être la mesure induite par la mesure d'entropie maximale sur la tour associée au code introduite par Hansel et Blanchard. Nous en déduisons des points génériques pour les systèmes sofiques et les θ-shifts munis de leur mesure maximale.

The Dimension of the Maximal Measure for a Polynomial Map

1984 ◽  
Vol 119 (2) ◽  
pp. 425 ◽  
Author(s):  
Anthony Manning
Keyword(s):  
Maximal Measure ◽  
Polynomial Map

scholarly journals MixingC rmaps of the interval without maximal measure

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