scholarly journals Measures of maximal entropy for suspension flows

2020 ◽  
Author(s):  
Godofredo Iommi ◽  
Anibal Velozo
Keyword(s):  
Maximal Entropy ◽  
Suspension Flows ◽  
Measures Of Maximal Entropy

scholarly journals Measures of maximal entropy for suspension flows over the full shift

2019 ◽  
Vol 294 (1-2) ◽  
pp. 769-781 ◽  
Author(s):  
Tamara Kucherenko ◽  
Daniel J. Thompson
Keyword(s):  
Maximal Entropy ◽  
Suspension Flows ◽  
Full Shift ◽  
Measures Of Maximal Entropy

Entropy and rotation sets: A toy model approach

2016 ◽  
Vol 18 (05) ◽  
pp. 1550083 ◽  
Author(s):  
Tamara Kucherenko ◽  
Christian Wolf
Keyword(s):  
Invariant Measures ◽  
Maximal Entropy ◽  
Probability Measures ◽  
Compact Metric Space ◽  
Lipschitz Continuous ◽  
Exposed Point ◽  
Continuous Potential ◽  
Rotation Set ◽  
Measures Of Maximal Entropy ◽  
Model Approach

Given a continuous dynamical system [Formula: see text] on a compact metric space [Formula: see text] and a continuous potential [Formula: see text], the generalized rotation set is the subset of [Formula: see text] consisting of all integrals of [Formula: see text] with respect to all invariant probability measures. The localized entropy at a point in the rotation set is defined as the supremum of the measure-theoretic entropies over all invariant measures whose integrals produce that point. In this paper, we provide an introduction to the theory of rotation sets and localized entropies. Moreover, we consider a shift map and construct a Lipschitz continuous potential, for which we are able to explicitly compute the geometric shape of the rotation set and its boundary measures. We show that at a particular exposed point on the boundary there are exactly two ergodic localized measures of maximal entropy.

A subshift of finite type that is equivalent to the Ising model

1995 ◽  
Vol 15 (3) ◽  
pp. 543-556 ◽  
Author(s):  
Olle Häggström
Keyword(s):  
Ising Model ◽  
Finite Type ◽  
Gibbs Measures ◽  
Ergodic Measure ◽  
Maximal Entropy ◽  
Subshift Of Finite Type ◽  
Translation Invariant ◽  
Measures Of Maximal Entropy ◽  
Natural Way ◽  
Measure Of Maximal Entropy

AbstractFor the Ising model with rational parameters we show how to construct a subshift of finite type that is equivalent to this Ising model, in that the translation invariant Gibbs measures for the Ising model and the measures of maximal entropy for the subshift of finite type can be identified in a natural way. This is generalized to the non-translation invariant case as well. We also show how to construct, given any H > 0, an ergodic measure of maximal entropy for a subshift of finite type and a continuous factor, such that the factor has entropy H.

scholarly journals On subshifts with slow forbidden word growth

2021 ◽  
pp. 1-30
Author(s):  
RONNIE PAVLOV
Keyword(s):  
Growth Rate ◽  
General Result ◽  
Slow Growth ◽  
Main Tool ◽  
Maximal Entropy ◽  
Large Measure ◽  
Slow Growth Rate ◽  
Dynamical Properties ◽  
Alpha Beta ◽  
Measures Of Maximal Entropy

Abstract In this work, we treat subshifts, defined in terms of an alphabet $\mathcal {A}$ and (usually infinite) forbidden list $\mathcal {F}$ , where the number of n-letter words in $\mathcal {F}$ has ‘slow growth rate’ in n. We show that such subshifts are well behaved in several ways; for instance, they are boundedly supermultiplicative in the sense of Baker and Ghenciu [Dynamical properties of S-gap shifts and other shift spaces. J. Math. Anal. Appl.430(2) (2015), 633–647] and they have unique measures of maximal entropy with the K-property and which satisfy Gibbs bounds on large (measure-theoretically) sets. The main tool in our proofs is a more general result, which states that bounded supermultiplicativity and a sort of measure-theoretic specification property together imply uniqueness of the measure of maximum entropy and our Gibbs bounds. We also show that some well-known classes of subshifts can be treated by our results, including the symbolic codings of $x \mapsto \alpha + \beta x$ (the so-called $\alpha $ - $\beta $ shifts of Hofbauer [Maximal measures for simple piecewise monotonic transformations. Z. Wahrsch. verw. Geb.52(3) (1980), 289–300]) and the bounded density subshifts of Stanley [Bounded density shifts. Ergod. Th. & Dynam. Sys.33(6) (2013), 1891–1928].

scholarly journals Extender sets and measures of maximal entropy for subshifts

2019 ◽  
Vol 100 (3) ◽  
pp. 1013-1033
Author(s):  
Felipe García‐Ramos ◽  
Ronnie Pavlov
Keyword(s):  
Maximal Entropy ◽  
Measures Of Maximal Entropy
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