Compensation functions for factors of shifts of finite type

Antonioli, John

doi:10.1017/etds.2014.63

Cited by 10 publications

(23 citation statements)

References 19 publications

(41 reference statements)

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“…Therefore the condition (1) implies (2). The condition (2) trivially implies (3). It remains to show that (3) implies (1).…”

Section: Decomposition Of Infinite-to-one Factor Codesmentioning

confidence: 92%

Decomposition of infinite-to-one factor codes and uniqueness of relative equilibrium states

Yoo¹

2018

Journal of Modern Dynamics

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We show that an arbitrary factor map π : X → Y on an irreducible subshift of finite type is a composition of a finite-to-one factor code and a class degree one factor code. Using this structure theorem on infinite-to-one factor codes, we then prove that any equilibrium state ν on Y for a potential function of sufficient regularity lifts to a unique measure of maximal relative entropy on X. This answers a question raised by Boyle and Petersen (for lifts of Markov measures) and generalizes the earlier known special case of finite-to-one factor codes.

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“…Therefore the condition (1) implies (2). The condition (2) trivially implies (3). It remains to show that (3) implies (1).…”

Section: Decomposition Of Infinite-to-one Factor Codesmentioning

confidence: 92%

Decomposition of infinite-to-one factor codes and uniqueness of relative equilibrium states

Yoo¹

2018

Journal of Modern Dynamics

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“…An ingredient in our proof is an observation made in the following result by Antonioli [3]. Given a relative equilibrium state µ of V with summable variation, he showed that if µ does not have full support and ν has, then one can construct a new measure µ ′ by routing parts of a point in X depending on outcomes of tossing a coin and the new measure has bigger h(µ ′ ) + V dµ ′ .…”

Section: Introductionmentioning

confidence: 95%

“…By using the same argument as in [3], or alternatively by moving the calculation to the derivative system induced on S…”

Section: Jump Extensionmentioning

confidence: 99%

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Relative equilibrium states and class degree

Allahbakhshi

Antonioli

Yoo

2017

Ergod. Th. Dynam. Sys.

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Abstract. Given a factor code π from a shift of finite type X onto a sofic shift Y , an ergodic measure ν on Y , and a function V on X with summable variation, we prove an invariant upper bound on the number of ergodic measures on X which project to ν and maximize h(µ) + V dµ among all measures in the fiber π −1 (ν). If ν is fully supported, this bound is the class degree of π. This generalizes a previous result for the special case of V = 0.

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“…Question 1. Given a subadditive sequence F = {log f n } ∞ n=1 on a compact metric space X, what are necessary and sufficient conditions for the existence of a continuous function h on X such that (1) lim…”

Section: Introductionmentioning

confidence: 99%

Relative pressure functions and their equilibrium states

Yayama¹

2021

Preprint

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For a subshift (X, σ X ) and a subadditive sequence F = {log fn} ∞ n=1 on X, we study equivalent conditions for the existence of h ∈ C(X) such that limn→∞(1/n) log fndµ = hdµ for every invariant measure µ on X. For this purpose, we first we study necessary and sufficient conditions for F to be an asymptotically additive sequence in terms of certain properties for periodic points. For a factor map π : X → Y , where (X, σ X ) is an irreducible shift of finite type and (Y, σ Y ) is a subshift, applying our results and the results obtained by Cuneo [9] on asymptotically additive sequences, we study the existence of h with regard to a subadditive sequence associated to a relative pressure function. This leads to a characterization of the existence of a certain type of continuous compensation function for a factor map between subshifts. As an application, we study the projection πµ of an invariant weak Gibbs measure µ for a continuous function on an irreducible shift of finite type.

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Compensation functions for factors of shifts of finite type

Cited by 10 publications

References 19 publications

Decomposition of infinite-to-one factor codes and uniqueness of relative equilibrium states

Decomposition of infinite-to-one factor codes and uniqueness of relative equilibrium states

Relative equilibrium states and class degree

Relative pressure functions and their equilibrium states

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