A class of Markov shifts which are Bernoulli shifts

We construct and study C*-algebras associated with subshifts in symbolic dynamics as a generalization of Cuntz–Krieger algebras for topological Markov shifts. We prove some universal properties for the C*-algebras and give a criterion for them to be simple and purely infinite. We also present an example of a C*-algebra coming from a subshift which is not conjugate to a Markov shift.

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Equilibrium states and zero temperature limit on topologically transitive countable Markov shifts

Transactions of the American Mathematical Society ◽

10.1090/tran/7291 ◽

2018 ◽

Vol 370 (12) ◽

pp. 8451-8465 ◽

Cited By ~ 2

Author(s):

Ricardo Freire ◽

Victor Vargas

Keyword(s):

Temperature Limit ◽

Equilibrium States ◽

Zero Temperature ◽

Topologically Transitive ◽

Markov Shifts ◽

Countable Markov Shifts

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Cantor Sets, Bernoulli Shifts and Linear Dynamics

Springer Proceedings in Mathematics & Statistics - Descriptive Topology and Functional Analysis ◽

10.1007/978-3-319-05224-3_10 ◽

2014 ◽

pp. 195-207 ◽

Cited By ~ 1

Author(s):

Salud Bartoll ◽

Félix Martínez-Giménez ◽

Marina Murillo-Arcila ◽

Alfredo Peris

Keyword(s):

Cantor Sets ◽

Linear Dynamics ◽

Bernoulli Shifts

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Irreducible complexity of iterated symmetric bimodal maps

Discrete Dynamics in Nature and Society ◽

10.1155/ddns.2005.69 ◽

2005 ◽

Vol 2005 (1) ◽

pp. 69-85 ◽

Cited By ~ 2

Author(s):

J. P. Lampreia ◽

R. Severino ◽

J. Sousa Ramos

Keyword(s):

Tree Structure ◽

Unimodal Maps ◽

Markov Shifts ◽

Irreducible Complexity ◽

The Family

We introduce a tree structure for the iterates of symmetric bimodal maps and identify a subset which we prove to be isomorphic to the family of unimodal maps. This subset is used as a second factor for a∗-product that we define in the space of bimodal kneading sequences. Finally, we give some properties for this product and study the∗-product induced on the associated Markov shifts.

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