countable markov shifts
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Nonlinearity ◽  
2021 ◽  
Vol 34 (7) ◽  
pp. 4819-4843
Author(s):  
Elmer R Beltrán ◽  
Rodrigo Bissacot ◽  
Eric O Endo




2020 ◽  
Vol 21 (02) ◽  
pp. 2150008
Author(s):  
Ana Rodrigues ◽  
Samuel Roth ◽  
Zuzana Roth

In this paper, we generalize the recently introduced concept of fair measure [M. Misiurewicz and A. Rodrigues, Counting preimages, Ergod. Theor. Dyn. Syst. 38 (2018) 1837–1856]. We study fair measures for Markov and mixing interval maps with countably many branches. We investigate them in terms of the recurrence properties of some underlying countable Markov shifts, both from the stochastic viewpoint and from the viewpoint of thermodynamical formalism. Finally, we move beyond the interval and look for fair measures for graph maps.



2019 ◽  
Vol 20 (04) ◽  
pp. 2050028
Author(s):  
Godofredo Iommi ◽  
Camilo Lacalle ◽  
Yuki Yayama

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.



2019 ◽  
Vol 17 (2) ◽  
pp. 267-295 ◽  
Author(s):  
Alejandro Mesón ◽  
Fernando Vericat




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