scholarly journals Constant-to-one and onto global maps of homomorphisms between strongly connected graphs

1983 ◽  
Vol 3 (3) ◽  
pp. 387-413 ◽  
Author(s):  
Masakazu Nasu
Keyword(s):  
Dynamical Systems ◽  
Finite Type ◽  
Directed Graphs ◽  
Topological Conjugacy ◽  
Subshift Of Finite Type ◽  
Connected Graphs ◽  
Strongly Connected ◽  
Subshifts Of Finite Type

AbstractThe global maps of homomorphisms of directed graphs are very closely related to homomorphisms of a class of symbolic dynamical systems called subshifts of finite type. In this paper, we introduce the concepts of ‘induced regular homomorphism’ and ‘induced backward regular homomorphism’ which are associated with every homomorphism between strongly connected graphs whose global map is finite-to-one and onto, and using them we study the structure of constant-to-one and onto global maps of homorphisms between strongly connected graphs and that of constant-to-one and onto homomorphisms of irreducible subshifts of finite type. We determine constructively, up to topological conjugacy, the subshifts of finite type which are constant-to-one extensions of a given irreducible subshift of finite type. We give an invariant for constant-to-one and onto homomorphisms of irreducible subshifts of finite type.

scholarly journals Automorphisms of one-sided subshifts of finite type

1990 ◽  
Vol 10 (3) ◽  
pp. 421-449 ◽  
Author(s):  
Mike Boyle ◽  
John Franks ◽  
Bruce Kitchens
Keyword(s):  
Automorphism Group ◽  
Finite Type ◽  
Finite Order ◽  
Subshift Of Finite Type ◽  
Finite Subgroups ◽  
Subshifts Of Finite Type

AbstractWe prove that the automorphism group of a one-sided subshift of finite type is generated by elements of finite order. For one-sided full shifts we characterize the finite subgroups of the automorphism group. For one-sided subshifts of finite type we show that there are strong restrictions on the finite subgroups of the automorphism group.

scholarly journals Finite group actions on shifts of finite type

1985 ◽  
Vol 5 (1) ◽  
pp. 1-25 ◽  
Author(s):  
R. L. Adler ◽  
B. Kitchens ◽  
B. H. Marcus
Keyword(s):  
Finite Group ◽  
Finite Type ◽  
Commutation Relation ◽  
Group Actions ◽  
Topological Conjugacy ◽  
Positive Entropy ◽  
Group Automorphism ◽  
Subshift Of Finite Type ◽  
Finite Group Actions ◽  
Shift Transformation

AbstractA continuous ℤ⊗TG action on a subshift of finite type consists of a subshift of finite type with its shift transformation, together with a group, G, of homeomorphisms of the subshift and a group automorphism T, so that the commutation relation σ ° g = Tg ° ∑A is any positive entropy subshift of finite type, G is any finite group and T is any automorphism of G then there is a non-trivial ℤ⊗TG action on ∑A. We then classify all such actions up to ‘almost topological‘ conjugacy.

scholarly journals Embedding subshifts of finite type into the Fibonacci–Dyck shift

2016 ◽  
Vol 37 (6) ◽  
pp. 1862-1886
Author(s):  
TOSHIHIRO HAMACHI ◽  
WOLFGANG KRIEGER
Keyword(s):  
Finite Type ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Subshift Of Finite Type ◽  
Subshifts Of Finite Type ◽  
Necessary And Sufficient

A necessary and sufficient condition is given for the existence of an embedding of an irreducible subshift of finite type into the Fibonacci–Dyck shift.

Uniform Sampling of Subshifts of Finite Type on Grids and Trees

2017 ◽  
Vol 28 (03) ◽  
pp. 263-287 ◽  
Author(s):  
Jean Mairesse ◽  
Irène Marcovici
Keyword(s):  
Finite Type ◽  
Nearest Neighbor ◽  
Sampling Methods ◽  
Probability Measures ◽  
Probabilistic Cellular Automata ◽  
Subshift Of Finite Type ◽  
Uniform Sampling ◽  
Subshifts Of Finite Type ◽  
Uniform Random Sampling ◽  
Insight Into

Let us color the vertices of the grid ℤd or the infinite regular tree 𝕋d, using a finite number of colors, with the constraint that some predefined pairs of colors are not allowed for adjacent vertices. The set of admissible colorings is called a nearest-neighbor subshift of finite type (SFT). We study “uniform” probability measures on SFT, with the motivation of having an insight into “typical” admissible configurations. We recall the known results on uniform measures on SFT on grids and we complete the picture by presenting some contributions to the description of uniform measures on SFT on 𝕋d. Then we focus on the problem of uniform random sampling of configurations of SFT. We propose a first method based on probabilistic cellular automata, which is valid under some restrictive conditions. Then we concentrate on the case of SFT on ℤ for which we propose several alternative sampling methods.

The Local Product Structure of Expansive Automorphisms of Solenoids and Their Associated C*-Algebras

1996 ◽  
Vol 48 (4) ◽  
pp. 692-709 ◽  
Author(s):  
Berndt Brenken
Keyword(s):  
Abelian Group ◽  
Dynamical Systems ◽  
Coordinate System ◽  
Finite Type ◽  
Crossed Product ◽  
C Algebras ◽  
Local Product ◽  
Subshifts Of Finite Type ◽  
Canonical Coordinate System ◽  
Canonical Coordinate

AbstractAn explicit description of a hyperbolic canonical coordinate system for an expansive automorphism of a compact connected abelian group is given. These dynamical systems are factors of subshifts of finite type. Some properties of the associated crossed product C*-algebra are discussed. In these examples, the C* -algebras of Ruelle are crossed product algebras.

scholarly journals NONSTATIONARY MIXING AND THE UNIQUE ERGODICITY OF ADIC TRANSFORMATIONS

2009 ◽  
Vol 09 (03) ◽  
pp. 335-391 ◽  
Author(s):  
ALBERT M. FISHER
Keyword(s):  
Markov Chain ◽  
Dynamical Systems ◽  
Finite Type ◽  
Weak Ergodicity ◽  
Subshift Of Finite Type ◽  
Topological Mixing ◽  
Markov Chain Theory ◽  
Inhomogeneous Markov Chain ◽  
Chain Theory ◽  
Uniquely Ergodic

We define topological and measure-theoretic mixing for nonstationary dynamical systems and prove that for a nonstationary subshift of finite type, topological mixing implies the minimality of any adic transformation defined on the edge space, while if the Parry measure sequence is mixing, the adic transformation is uniquely ergodic. We also show this measure theoretic mixing is equivalent to weak ergodicity of the edge matrices in the sense of inhomogeneous Markov chain theory.

Support stability of maximizing measures for shifts of finite type

2019 ◽  
pp. 1-12
Author(s):  
JULIANO S. GONSCHOROWSKI ◽  
ANTHONY QUAS ◽  
JASON SIEFKEN
Keyword(s):  
Finite Type ◽  
Fundamental Difference ◽  
Probability Measures ◽  
Two Dimensional ◽  
Small Perturbations ◽  
Subshift Of Finite Type ◽  
Local Configuration ◽  
Ergodic Optimization ◽  
Full Shift ◽  
Subshifts Of Finite Type

This paper establishes a fundamental difference between $\mathbb{Z}$ subshifts of finite type and $\mathbb{Z}^{2}$ subshifts of finite type in the context of ergodic optimization. Specifically, we consider a subshift of finite type $X$ as a subset of a full shift  $F$ . We then introduce a natural penalty function  $f$ , defined on  $F$ , which is 0 if the local configuration near the origin is legal and $-1$ otherwise. We show that in the case of $\mathbb{Z}$ subshifts, for all sufficiently small perturbations, $g$ , of  $f$ , the $g$ -maximizing invariant probability measures are supported on $X$ (that is, the set $X$ is stably maximized by  $f$ ). However, in the two-dimensional case, we show that the well-known Robinson tiling fails to have this property: there exist arbitrarily small perturbations, $g$ , of  $f$ for which the $g$ -maximizing invariant probability measures are supported on $F\setminus X$ .

scholarly journals Zero-temperature limit of one-dimensional Gibbs states via renormalization: the case of locally constant potentials

2010 ◽  
Vol 31 (4) ◽  
pp. 1109-1161 ◽  
Author(s):  
J.-R. CHAZOTTES ◽  
J.-M. GAMBAUDO ◽  
E. UGALDE
Keyword(s):  
Finite Type ◽  
Recursive Algorithm ◽  
Temperature Limit ◽  
Finite Union ◽  
Subshift Of Finite Type ◽  
Frobenius Theorem ◽  
The Family ◽  
Finite Set ◽  
Constant Potential ◽  
Subshifts Of Finite Type

AbstractLet A be a finite set and let ϕ:Aℤ→ℝ be a locally constant potential. For each β>0 (‘inverse temperature’), there is a unique Gibbs measure μβϕ. We prove that as β→+∞, the family (μβϕ)β>0 converges (in the weak-* topology) to a measure that we characterize. This measure is concentrated on a certain subshift of finite type, which is a finite union of transitive subshifts of finite type. The two main tools are an approximation by periodic orbits and the Perron–Frobenius theorem for matrices à la Birkhoff. The crucial idea we bring is a ‘renormalization’ procedure which explains convergence and provides a recursive algorithm for computing the weights of the ergodic decomposition of the limit.

scholarly journals Lower entropy factors of sofic systems

1983 ◽  
Vol 3 (4) ◽  
pp. 541-557 ◽  
Author(s):  
Mike Boyle
Keyword(s):  
Periodic Point ◽  
Finite Type ◽  
Embedding Theorem ◽  
Subshift Of Finite Type ◽  
Sofic Shift ◽  
Sofic Shifts ◽  
Continuous Maps ◽  
Lower Entropy ◽  
Subshifts Of Finite Type ◽  
General Method

AbstractA mixing subshift of finite type T is a factor of a sofic shift S of greater entropy if and only if the period of any periodic point of S is divisible by the period of some periodic point of T. Mixing sofic shifts T satisfying this theorem are characterized, as are those mixing sofic shifts for which Krieger's Embedding Theorem holds. These and other results rest on a general method for extending shift-commuting continuous maps into mixing subshifts of finite type.

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