Factors of Gibbs measures for subshifts of finite type

2011 ◽  
Vol 43 (4) ◽  
pp. 751-764 ◽  
Author(s):  
Thomas M. W. Kempton
Keyword(s):  
Finite Type ◽  
Gibbs Measures ◽  
Subshifts Of Finite Type

scholarly journals Gibbs and equilibrium measures for some families of subshifts

2012 ◽  
Vol 33 (3) ◽  
pp. 934-953 ◽  
Author(s):  
TOM MEYEROVITCH
Keyword(s):  
Finite Type ◽  
Gibbs Measure ◽  
Equilibrium Measure ◽  
Gibbs Measures ◽  
Type Theorem ◽  
Equilibrium Measures ◽  
Strongly Irreducible ◽  
Subshifts Of Finite Type ◽  
Summable Variation

AbstractFor subshifts of finite type (SFTs), any equilibrium measure is Gibbs, as long as $f$ has $d$-summable variation. This is a theorem of Lanford and Ruelle. Conversely, a theorem of Dobrušin states that for strongly irreducible subshifts, shift-invariant Gibbs measures are equilibrium measures. Here we prove a generalization of the Lanford–Ruelle theorem: for all subshifts, any equilibrium measure for a function with $d$-summable variation is ‘topologically Gibbs’. This is a relaxed notion which coincides with the usual notion of a Gibbs measure for SFTs. In the second part of the paper, we study Gibbs and equilibrium measures for some interesting families of subshifts: $\beta $-shifts, Dyck shifts and Kalikow-type shifts (defined below). In all of these cases, a Lanford–Ruelle-type theorem holds. For each of these families, we provide a specific proof of the result.

scholarly journals Micromeasure distributions and applications for conformally generated fractals

2015 ◽  
Vol 159 (3) ◽  
pp. 547-566 ◽  
Author(s):  
JONATHAN M. FRASER ◽  
MARK POLLICOTT
Keyword(s):  
Finite Type ◽  
Julia Sets ◽  
Gibbs Measures ◽  
Schottky Groups ◽  
Limit Sets ◽  
Distance Set ◽  
Self Similar ◽  
Subshifts Of Finite Type

AbstractWe study the scaling scenery of Gibbs measures for subshifts of finite type on self-conformal fractals and applications to Falconer's distance set problem and dimensions of projections. Our analysis includes hyperbolic Julia sets, limit sets of Schottky groups and graph-directed self-similar sets.

Ruelle's transfer operator for random subshifts of finite type

1995 ◽  
Vol 15 (3) ◽  
pp. 413-447 ◽  
Author(s):  
Thomas Bogenschütz ◽  
Volker Mathias Gundlach
Keyword(s):  
Dynamical Systems ◽  
Finite Type ◽  
Invariant Measures ◽  
Gibbs Measures ◽  
Transfer Operator ◽  
Selection Procedure ◽  
Probability Measures ◽  
Random Functions ◽  
Subshifts Of Finite Type ◽  
Definition Of

AbstractWe consider a Ruelle—Perron—Frobenius type of selection procedure for probability measures that are invariant under random subshifts of finite type. In particular we prove that for a class of random functions this method leads to a unique probability exhibiting properties that justify the names Gibbs measure and equilibrium states. In order to do this we introduce the notion of bundle random dynamical systems and provide a theory for their invariant measures as well as give a precise definition of Gibbs measures.

Subshifts of finite type

1976 ◽  
pp. 117-130
Author(s):  
Manfred Denker ◽  
Christian Grillenberger ◽  
Karl Sigmund
Keyword(s):  
Finite Type ◽  
Subshifts Of Finite Type

Endomorphisms of irreducible subshifts of finite type

1974 ◽  
Vol 8 (2) ◽  
pp. 167-175 ◽  
Author(s):  
Ethan M. Coven ◽  
Michael E. Paul
Keyword(s):  
Finite Type ◽  
Subshifts Of Finite Type

Chaos for Subshifts of Finite Type

2005 ◽  
Vol 21 (6) ◽  
pp. 1407-1414 ◽  
Author(s):  
Huo Yun Wang ◽  
Jin Cheng Xiong
Keyword(s):  
Finite Type ◽  
Subshifts Of Finite Type
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