Systèmes codés

Blanchard, F.; Hansel, Georges

doi:10.1016/0304-3975(86)90108-8

Cited by 136 publications

(107 citation statements)

References 11 publications

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“…We begin by recalling the relationship between shift spaces and languages. We refer the reader to [BH86,LM95] for further background and proofs.…”

Section: Definitions and Statement Of Resultsmentioning

confidence: 99%

“…Generically, then, a β-shift is not sofic and does not possess the specification property [BM86,Sch97]. Every β-shift can be presented by a countable state directed labeled graph Γ β , which is shown in Figure 1 (see also [BH86,PS07,Tho10]). We describe the construction of this graph, assuming that w(β) is not eventually periodic.…”

Section: Statement Of Resultsmentioning

confidence: 99%

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Intrinsic ergodicity beyond specification: β-shifts, S-gap shifts, and their factors

2012

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Abstract. We give sufficient conditions for a shift space (Σ, σ) to be intrinsically ergodic, along with sufficient conditions for every subshift factor of Σ to be intrinsically ergodic. As an application, we show that every subshift factor of a β-shift is intrinsically ergodic, which answers an open question included in Mike Boyle's article "Open problems in symbolic dynamics". We obtain the same result for S-gap shifts, and describe an application of our conditions to more general coded systems. One novelty of our approach is the introduction of a new version of the specification property that is well adapted to the study of symbolic spaces with a non-uniform structure.

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“…We begin by recalling the relationship between shift spaces and languages. We refer the reader to [BH86,LM95] for further background and proofs.…”

Section: Definitions and Statement Of Resultsmentioning

confidence: 99%

Section: Statement Of Resultsmentioning

confidence: 99%

Intrinsic ergodicity beyond specification: β-shifts, S-gap shifts, and their factors

2012

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“…The even shift is an example of a sofic system. A subshift Σ is called a coded system if it can be represented by an irreducible countable labeled graph [3]. We do not know if every sofic system, or even if every coded system is an exclusion subshift.…”

Section: Sfts and Sofic Systemsmentioning

confidence: 99%

“…A subshift Σ is called a coded system if it is topologically conjugate to the shift on an irreducible countable labeled graph [3]. Equivalently, Σ is called coded if Σ contains an increasing sequence of irreducible subshifts of finite type (SFTs) whose union is dense in Σ [4].…”

Section: Coded Systemsmentioning

confidence: 99%

Topological and symbolic dynamics for hyperbolic systems with holes

Bundfuss

Krüger

Troubetzkoy

2010

Ergod. Th. Dynam. Sys.

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Abstract. We consider an Axiom A diffeomorphism or a Markov map of an interval and the invariant set Ω * of orbits which never falls into a fixed hole. We study various aspects of the symbolic representation of Ω * and of its nonwandering set Ω nw . Our results are on the cardinality of the set of topologically transitive components of Ω nw and their structure. We also prove that Ω * is generically a subshift of finite type in several senses.

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“…To avoid ambiguities, we consider the syntactic semigroup of a full shift to be the trivial semigroup. On the other hand, if X is a subshift of A Z different from a full shift then the syntactic semigroup of L(X ) is independent of A, basically because all elements of the non-empty set A + \ L(X ) are in the same class of the syntactic congruence, which is a zero of the syntactic semigroup [8]. For a pseudovariety V, consider the class S (V) of subshifts X whose syntactic semigroup belongs to V. …”

Section: Classes Of Sofic Subshifts Closed Under Taking Divisorsmentioning

confidence: 99%

A new algebraic invariant for weak equivalence of sofic subshifts

Chaubard

Costa

2008

RAIRO-Theor. Inf. Appl.

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It is studied how taking the inverse image by a sliding block code affects the syntactic semigroup of a sofic subshift. Two independent approaches are used: ζ-semigroups as recognition structures for sofic subshifts, and relatively free profinite semigroups. A new algebraic invariant is obtained for weak equivalence of sofic subshifts, by determining which classes of sofic subshifts naturally defined by pseudovarieties of finite semigroups are closed under weak equivalence. Among such classes are the classes of almost finite type subshifts and aperiodic subshifts. The algebraic invariant is compared with other robust conjugacy invariants.

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Systèmes codés

Cited by 136 publications

References 11 publications

Intrinsic ergodicity beyond specification: β-shifts, S-gap shifts, and their factors

Intrinsic ergodicity beyond specification: β-shifts, S-gap shifts, and their factors

Topological and symbolic dynamics for hyperbolic systems with holes

A new algebraic invariant for weak equivalence of sofic subshifts

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