On the finitary isomorphisms of markov shifts that have finite expected coding time

1983 ◽  
Vol 65 (2) ◽  
pp. 323-328 ◽  
Author(s):  
Wolfgang Krieger
Keyword(s):  
Markov Shifts ◽  
Finitary Isomorphisms

scholarly journals A return time invariant for finitary isomorphisms

1984 ◽  
Vol 4 (2) ◽  
pp. 225-231 ◽  
Author(s):  
U. R. Fiebig
Keyword(s):  
Finite Measure ◽  
Measurable Subset ◽  
Return Time ◽  
Time Function ◽  
Markov Shifts ◽  
Measure Preserving Transformation ◽  
Recurrence Theorem ◽  
First Return Time ◽  
Time Invariant ◽  
Finitary Isomorphisms

AbstractPoincare's recurrence theorem says that, given a measurable subset of a space on which a finite measure-preserving transformation acts, almost every point of the subset returns to the subset after a finite number of applications of the transformation. Moreover, Kac's recurrence theorem refines this result by showing that the average of the first return times to the subset over the subset is at most one, with equality in the ergodic case. In particular, the first return time function to any measurable set is integrable. By considering the supremum over all p ≥ 1 for which the first return time function is p-integrable for all open sets, we obtain a number for each almost-topological dynamical system, which we call the return time invariant. It is easy to show that this invariant is non-decreasing under finitary homomorphism. We use the invariant to construct a continuum number of countable state Markov shifts with a given entropy (and hence measure-theoretically isomorphic) which are pairwise non-finitarily isomorphic.

Finitary isomorphisms of irreducible Markov shifts

1979 ◽  
Vol 34 (4) ◽  
pp. 281-286 ◽  
Author(s):  
Michael Keane ◽  
Meir Smorodinsky
Keyword(s):  
Markov Shifts ◽  
Finitary Isomorphisms

On C*-Algebras Associated with Subshifts

1997 ◽  
Vol 08 (03) ◽  
pp. 357-374 ◽  
Author(s):  
Kengo Matsumoto
Keyword(s):  
Symbolic Dynamics ◽  
Markov Shift ◽  
C Algebra ◽  
C Algebras ◽  
Markov Shifts ◽  
Universal Properties

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.

scholarly journals Irreducible complexity of iterated symmetric bimodal maps

2005 ◽  
Vol 2005 (1) ◽  
pp. 69-85 ◽  
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.

scholarly journals A class of Markov shifts which are Bernoulli shifts

1971 ◽  
Vol 6 (3) ◽  
pp. 323-328 ◽  
Author(s):  
Robert McCabe ◽  
Paul Shields
Keyword(s):  
Bernoulli Shifts ◽  
Markov Shifts

Markov shifts and topological entropy of families of homoclinic tangles

2019 ◽  
Vol 266 (12) ◽  
pp. 8492-8518
Author(s):  
Bráulio Garcia ◽  
Valentín Mendoza
Keyword(s):  
Topological Entropy ◽  
Markov Shifts ◽  
Homoclinic Tangles
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