scholarly journals Thermodynamic formalism for random countable Markov shifts

2008 ◽  
Vol 22 (1/2, September) ◽  
pp. 131-164 ◽  
Author(s):  
Manuel Stadlbauer ◽  
Yuri Kifer ◽  
Manfred Denker
Keyword(s):  
Thermodynamic Formalism ◽  
Markov Shifts ◽  
Countable Markov Shifts

scholarly journals Corrigendum to: Thermodynamic formalism for random countable Markov shifts

2015 ◽  
Vol 35 (1) ◽  
pp. 593-594 ◽  
Author(s):  
Manfred Denker ◽  
◽  
Yuri Kifer ◽  
Manuel Stadlbauer ◽  
◽  
...  
Keyword(s):  
Thermodynamic Formalism ◽  
Markov Shifts ◽  
Countable Markov Shifts

scholarly journals Almost-additive thermodynamic formalism for countable Markov shifts

Nonlinearity ◽  
2011 ◽  
Vol 25 (1) ◽  
pp. 165-191 ◽  
Author(s):  
Godofredo Iommi ◽  
Yuki Yayama
Keyword(s):  
Thermodynamic Formalism ◽  
Markov Shifts ◽  
Countable Markov Shifts

scholarly journals Recurrence and pressure for group extensions

2014 ◽  
Vol 36 (1) ◽  
pp. 108-126 ◽  
Author(s):  
JOHANNES JAERISCH
Keyword(s):  
Multiplicative Group ◽  
Thermodynamic Formalism ◽  
Kleinian Groups ◽  
Base Space ◽  
Real Numbers ◽  
Group Extensions ◽  
Markov Shifts ◽  
Group Presentations ◽  
Equivalent Conditions ◽  
Countable Markov Shifts

We investigate the thermodynamic formalism for recurrent potentials on group extensions of countable Markov shifts. Our main result characterizes recurrent potentials depending only on the base space, in terms of the existence of a conservative product measure and a homomorphism from the group into the multiplicative group of real numbers. We deduce that, for a recurrent potential depending only on the base space, the group is necessarily amenable. Moreover, we give equivalent conditions for the base pressure and the skew product pressure to coincide. Finally, we apply our results to analyse the Poincaré series of Kleinian groups and the cogrowth of group presentations.

scholarly journals Hidden Gibbs measures on shift spaces over countable alphabets

2019 ◽  
Vol 20 (04) ◽  
pp. 2050028
Author(s):  
Godofredo Iommi ◽  
Camilo Lacalle ◽  
Yuki Yayama
Keyword(s):  
Variational Principle ◽  
Existence And Uniqueness ◽  
Gibbs Measures ◽  
Thermodynamic Formalism ◽  
Topological Pressure ◽  
Markov Shifts ◽  
Sofic Shifts ◽  
Uniqueness Of Equilibrium ◽  
Countable Markov Shifts ◽  
Generalized Gibbs Measures

We study the thermodynamic formalism for particular types of sub-additive sequences on a class of subshifts over countable alphabets. The subshifts we consider include factors of irreducible countable Markov shifts under certain conditions, which we call irreducible countable sofic shifts. We show the variational principle for topological pressure for some sub-additive sequences with tempered variation on irreducible countable sofic shifts. We also study conditions for the existence and uniqueness of invariant ergodic Gibbs measures and the uniqueness of equilibrium states. Applications are given to some dimension problems and study of factors of (generalized) Gibbs measures on certain subshifts over countable alphabets.

scholarly journals On the existence of maximizing measures for irreducible countable Markov shifts: a dynamical proof

2013 ◽  
Vol 34 (4) ◽  
pp. 1103-1115 ◽  
Author(s):  
RODRIGO BISSACOT ◽  
RICARDO DOS SANTOS FREIRE
Keyword(s):  
Probability Measure ◽  
Bounded Variation ◽  
Finite Alphabet ◽  
Markov Shift ◽  
Positive Real ◽  
Shift Space ◽  
Markov Shifts ◽  
Maximizing Measure ◽  
Full Shift ◽  
Countable Markov Shifts

AbstractWe prove that if ${\Sigma }_{\mathbf{A} } ( \mathbb{N} )$ is an irreducible Markov shift space over $ \mathbb{N} $ and $f: {\Sigma }_{\mathbf{A} } ( \mathbb{N} )\rightarrow \mathbb{R} $ is coercive with bounded variation then there exists a maximizing probability measure for $f$, whose support lies on a Markov subshift over a finite alphabet. Furthermore, the support of any maximizing measure is contained in this same compact subshift. To the best of our knowledge, this is the first proof beyond the finitely primitive case in the general irreducible non-compact setting. It is also noteworthy that our technique works for the full shift over positive real sequences.

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