scholarly journals Periodic-finite-type shift spaces

2002 ◽  
Author(s):  
B. Moision ◽  
P.H. Siegel
Keyword(s):  
Finite Type ◽  
Shift Spaces ◽  
Type Shift

scholarly journals Periodic-Finite-Type Shift Spaces

2011 ◽  
Vol 57 (6) ◽  
pp. 3677-3691 ◽  
Author(s):  
Marie-Pierre Beal ◽  
Maxime Crochemore ◽  
Bruce E. Moision ◽  
Paul H. Siegel
Keyword(s):  
Finite Type ◽  
Shift Spaces ◽  
Type Shift

Tilings, fundamental cocycles and fundamental groups of symbolic ${\Bbb Z}^{d}$-actions

1998 ◽  
Vol 18 (6) ◽  
pp. 1473-1525 ◽  
Author(s):  
KLAUS SCHMIDT
Keyword(s):  
Finite Type ◽  
Homomorphic Image ◽  
Discrete Group ◽  
Fundamental Groups ◽  
Two Dimensional ◽  
Shift Spaces ◽  
Shift Space ◽  
Topologically Mixing

We prove that certain topologically mixing two-dimensional shifts of finite type have a ‘fundamental’ $1$-cocycle with the property that every continuous $1$-cocycle on the shift space with values in a discrete group is continuously cohomologous to a homomorphic image of the fundamental cocycle. These fundamental cocycles are closely connected with representations of the shift space by Wang tilings and the tiling groups of Conway, Lagarias and Thurston, and they determine the projective fundamental groups of the shift spaces introduced by Geller and Propp.

scholarly journals Decompositions of factor codes and embeddings between shift spaces with unequal entropies

2012 ◽  
Vol 33 (1) ◽  
pp. 144-157
Author(s):  
SOONJO HONG ◽  
UIJIN JUNG ◽  
IN-JE LEE
Keyword(s):  
Finite Type ◽  
Shift Spaces ◽  
Sofic Shift ◽  
Shift Space ◽  
Sofic Shifts ◽  
The Given ◽  
Factor Code

AbstractGiven a factor code between sofic shifts X and Y, there is a family of decompositions of the original code into factor codes such that the entropies of the intermediate subshifts arising from the decompositions are dense in the interval from the entropy of Y to that of X. Furthermore, if X is of finite type, we can choose those intermediate subshifts as shifts of finite type. In the second part of the paper, given an embedding from a shift space to an irreducible sofic shift, we characterize the set of the entropies of the intermediate subshifts arising from the decompositions of the given embedding into embeddings.

scholarly journals Orbit Growth of Periodic-Finite-Type Shifts via Artin–Mazur Zeta Function

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 685
Author(s):  
Azmeer Nordin ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Dynamical System ◽  
Asymptotic Behavior ◽  
Zeta Function ◽  
Finite Type ◽  
Discrete Dynamical System ◽  
Closed Orbits ◽  
Counting Functions ◽  
Type Shift

The prime orbit and Mertens’ orbit counting functions describe the growth of closed orbits in a discrete dynamical system in a certain way. In this paper, we prove the asymptotic behavior of these functions for a periodic-finite-type shift. The proof relies on the meromorphic extension of its Artin–Mazur zeta function.

A Comparative Study of Periods in a Periodic-Finite-Type Shift

2009 ◽  
Vol 23 (3) ◽  
pp. 1507-1524 ◽  
Author(s):  
Akiko Manada ◽  
Navin Kashyap
Keyword(s):  
Comparative Study ◽  
Finite Type ◽  
Type Shift

Measures of maximal relative entropy with full support

2010 ◽  
Vol 31 (6) ◽  
pp. 1889-1899 ◽  
Author(s):  
JISANG YOO
Keyword(s):  
Probability Measure ◽  
Finite Type ◽  
Relative Entropy ◽  
Invariant Probability Measure ◽  
Shift Of Finite Type ◽  
Shift Spaces ◽  
Full Support ◽  
Shift Space ◽  
Sofic Shifts ◽  
Factor Map

AbstractLet π be a factor map from an irreducible shift of finite type X to a shift space Y. Let ν be an invariant probability measure on Y with full support. We show that every measure on X of maximal relative entropy over ν is fully supported. As a result, given any invariant probability measure ν on Y with full support, there is an invariant probability measure μ on X with full support that maps to ν under π. If ν is ergodic, μ can be chosen to be ergodic. These results can be generalized to the case of sofic shifts. We demonstrate that the results do not extend to general shift spaces by providing counterexamples.

MIXING PROPERTY AND ENTROPY CONJUGACY OF ℤ2 SUBSHIFT OF FINITE TYPE: A CASE STUDY

2009 ◽  
Vol 19 (09) ◽  
pp. 2979-2991
Author(s):  
JUNG-CHAO BAN ◽  
SZU-YU LIN ◽  
YIN-HENG LIN
Keyword(s):  
Finite Type ◽  
Type A ◽  
Subshift Of Finite Type ◽  
Shift Spaces ◽  
Mixing Property

In the paper, the mixing property of ℤ2 subshift of finite type (SFT) is studied, some checkable conditions are provided to examine the property of mixing. Once the mixing property is checked, a class of examples can be found to show it possesses an entropy conjugacy property proposed in [Quas & Trow, 2000]. Finally, we construct an example of two shift spaces X and Y that are entropy conjugate but not conjugate.

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