Quantified block gluing for multidimensional subshifts of finite type: aperiodicity and entropy

2021 ◽  
Author(s):  
Silvere Gangloff ◽  
Mathieu Sablik
Keyword(s):  
Finite Type ◽  
Subshifts Of Finite Type

Subshifts of finite type

1976 ◽  
pp. 117-130
Author(s):  
Manfred Denker ◽  
Christian Grillenberger ◽  
Karl Sigmund
Keyword(s):  
Finite Type ◽  
Subshifts Of Finite Type

Endomorphisms of irreducible subshifts of finite type

1974 ◽  
Vol 8 (2) ◽  
pp. 167-175 ◽  
Author(s):  
Ethan M. Coven ◽  
Michael E. Paul
Keyword(s):  
Finite Type ◽  
Subshifts Of Finite Type

Chaos for Subshifts of Finite Type

2005 ◽  
Vol 21 (6) ◽  
pp. 1407-1414 ◽  
Author(s):  
Huo Yun Wang ◽  
Jin Cheng Xiong
Keyword(s):  
Finite Type ◽  
Subshifts Of Finite Type

scholarly journals Chains, entropy, coding

1986 ◽  
Vol 6 (3) ◽  
pp. 415-448 ◽  
Author(s):  
Karl Petersen
Keyword(s):  
Growth Rate ◽  
Markov Chains ◽  
Random Walks ◽  
Finite Type ◽  
Periodic Orbits ◽  
Entropy Coding ◽  
Positive Entropy ◽  
Loop Analysis ◽  
Countable State ◽  
Subshifts Of Finite Type

AbstractVarious definitions of the entropy for countable-state topological Markov chains are considered. Concrete examples show that these quantities do not coincide in general and can behave badly under nice maps. Certain restricted random walks which arise in a problem in magnetic recording provide interesting examples of chains. Factors of some of these chains have entropy equal to the growth rate of the number of periodic orbits, even though they contain no subshifts of finite type with positive entropy; others are almost sofic – they contain subshifts of finite type with entropy arbitrarily close to their own. Attempting to find the entropies of such subshifts of finite type motivates the method of entropy computation by loop analysis, in which it is not necessary to write down any matrices or evaluate any determinants. A method for variable-length encoding into these systems is proposed, and some of the smaller subshifts of finite type inside these systems are displayed.

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