101 research outputs found
A new algebraic invariant for weak equivalence of sofic subshifts
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.Research programme AutoMathA of ESF; Pessoa bilateral project Egide/Grices 11113YM "Automata, profinite semigroups and symbolic dynamics"; FCT, grant SFRH/BD/24200/2005; POCI 2010; FS
A new algebraic invariant for weak equivalence of sofic subshifts
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.Research programme AutoMathA of ESF; Pessoa bilateral project Egide/Grices 11113YM "Automata, profinite semigroups and symbolic dynamics"; FCT, grant SFRH/BD/24200/2005; POCI 2010; FS
Finite type approximations of Gibbs measures on sofic subshifts
Consider a H\"older continuous potential defined on the full shift
A^\nn, where is a finite alphabet. Let X\subset A^\nn be a specified
sofic subshift. It is well-known that there is a unique Gibbs measure
on associated to . Besides, there is a natural nested
sequence of subshifts of finite type converging to the sofic subshift
. To this sequence we can associate a sequence of Gibbs measures
. In this paper, we prove that these measures weakly converge
at exponential speed to (in the classical distance metrizing weak
topology). We also establish a strong mixing property (ensuring weak
Bernoullicity) of . Finally, we prove that the measure-theoretic
entropy of converges to the one of exponentially fast.
We indicate how to extend our results to more general subshifts and potentials.
We stress that we use basic algebraic tools (contractive properties of iterated
matrices) and symbolic dynamics.Comment: 18 pages, no figure
Sofic-Dyck shifts
We define the class of sofic-Dyck shifts which extends the class of
Markov-Dyck shifts introduced by Inoue, Krieger and Matsumoto. Sofic-Dyck
shifts are shifts of sequences whose finite factors form unambiguous
context-free languages. We show that they correspond exactly to the class of
shifts of sequences whose sets of factors are visibly pushdown languages. We
give an expression of the zeta function of a sofic-Dyck shift
Expansive actions of countable amenable groups, homoclinic pairs, and the Myhill property
Let be a compact metrizable space equipped with a continuous action of a
countable amenable group . Suppose that the dynamical system is
expansive and is the quotient by a uniformly bounded-to-one factor map of a
strongly irreducible subshift. Let be a continuous map
commuting with the action of . We prove that if there is no pair of distinct
-homoclinic points in having the same image under , then is
surjective.Comment: arXiv admin note: text overlap with arXiv:1506.0694
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