![]() "A geometric interpretation of the Schützenberger group of a minimal subshift." Ark. countable amenable group and A is a finite set, then every strongly irreducible subshift AG has the Myhill property. ![]() Work partially supported respectively by CMUP (UID/MAT/00144/2013) and CMUC (UID/MAT/00324/2013), which are funded by FCT (Portugal) with national (MCTES) and European structural funds through the programs FEDER, under the partnership agreement PT2020. A complete set of computable invariants is given for deciding whether two irreducible subshifts of finite type have topologically equivalent suspension. For an irreducible subshift of finite type, the value of this measure on a basic cylinder set is easily. Also, when people say 'subshift of finite type' they're usually talking about a slightly more complicated structure: not just the set of sequences, but also a particular topology on that set (namely, the one induced by the Tychonoff product topology on \Sigman ) and a shift map \sigma, which slides a sequence to the left (or, in the one. A further result involving geometric arguments on Rauzy graphs is a criterion for freeness of the profinite group of a minimal subshift based on the Return Theorem of Berthé et al. They are examples of intrinsically ergodic flows, i.e., flows having a unique invariant measure such that the topological entropy of the flow is finite and equal to the measure-theoretic entropy with respect to the distinguished measure. Every strongly irreducible subshift is topologically transitive. We prove that if XAG is a strongly irreducible subshift then X has the Myhill property, that is, every pre-injective cellular automaton :XX is surjective. It provides a subshift over and a Hilbert C-bimodule H A over A which gives rise to a C-algebra O as a Cuntz-Pimsner algebra (11, cf. A subshift of KG is a closed, G-invariant subspace. Indeed, the group is shown to be isomorphic to the inverse limit of the profinite completions of the fundamental groups of the Rauzy graphs of the subshift. Let G be an amenable group and let A be a finite set. Given an irreducible subshift of nite type X, a sub- shift Y, a factor map : X Y, and an ergodic invariant measure on Y, there can exist more than one ergodic measure on X which projects to and has maximal entropy among all measures in the ber, but there is an explicit bound on the number of such maximal entropy preimages. In the case of minimal subshifts, the same group is shown in the present paper to also arise from geometric considerations involving the Rauzy graphs of the subshift. The group in question was initially obtained as a maximal subgroup of a free profinite semigroup. ![]() In this case we need the strong separation condition and can only prove that the packing measure and δ \delta δ-approximate packing pre-measure coincide for sufficiently small δ > 0 \delta>0 δ > 0.The first author has associated in a natural way a profinite group to each irreducible subshift. A graph is irreducible provided there is a vertex path between any two. Finally we consider an analogous version of the problem for packing measure. this case the resulting shift space of itineraries is a subshift of finite type. We also give applications of our results concerning Ahlfors regularity. Weiss, Subshifts of finite type and sofic systems, Monats. Thus, this repelling tree is self-similar (in the sense of graph directed constructions). For example, it fails in general for self-conformal sets, self-affine sets and Julia sets. chosen strongly connected, the sofic shift is said to be irreducible. Abstract: The self-similar structure of the attracting subshift of a primitive substitution is carried over to the limit set of the repelling tree in the boundary of Outer Space of the corresponding irreducible outer automorphism of a free group. ![]() We also give several examples showing that one cannot hope for the equality to hold in general if one moves in a number of the natural directions away from ‘self-similar’. The main tool in the proof is an exhaustion lemma for Hausdorff measure based on the Vitali Covering Theorem. For a subshift Z AG, we say Z is strongly irreducible iff iZ is. Our main result shows that this equality holds for any subset of a self-similar set corresponding to a nontrivial cylinder of an irreducible subshift of finite type, and thus also for any self-similar or graph-directed self-similar set, regardless of separation conditions. Some basic facts about strongly irreducible subshifts. We are interested in situations where the Hausdor measure and Hausdorff content of a set are equal in the critical dimension. ![]()
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