![]() ![]() Salimov, On Rauzy graph sequences of infinite words, J. G. Rauzy, Seminar on Number Theory (Université Bordeaux I, Talence, 1983) p.View on Springer Save to Library Create Alert On the density of periodic configurations in strongly irreducible subshifts T. Pin, Varieties of Formal Languages ( Plenum, London, 1986 ). We prove that if X AG is a strongly irreducible subshift then X has the Myhill property, that is, every pre-injective cellular automaton : X X is surjective. J.-J. Pansiot, Automata, Languages and Programming, Lecture Notes in Computer Science 172 (Springer, 1984) pp.Lothaire, Algebraic Combinatorics on Words ( Cambridge University Press, Cambridge, UK, 2002 ). Fogg, Substitutions in Dynamics, Arithmetics and Combinatorics, Lecture Notes in Mathematics 1794 ( Springer-Verlag, Berlin, 2002 ). Reutenauer, Codes and Automata, Encyclopedia of Mathematics and its Applications 129 ( Cambridge University Press, Cambridge, 2010 ). 12, 371 (2002), DOI: 10.1142/S021819670200095X. Irreducible subshifts have unique measures of maximal entropy if they are for instance of finite type or sofic (factors of shifts of finite type). Costa, Presentations of Schützenberger groups of minimal subshifts, Technical Report CMUP 2010-1, University of Porto (2010). Valery B. Kudryavtsev and Ivo G. Rosenberg (Springer, 2005) pp. J. Almeida, Structural Theory of Automata, Semigroups, and Universal Algebra, NATO Science Series II: Mathematics, Physics and Chemistry 207, eds.(Fundamental and Applied Mathematics) 11(3) (2005) 13–48 (in Russian) J. Thus, this repelling tree is self-similar (in the sense of graph directed constructions). Almeida, Profinite groups associated with weakly primitive substitutions, Fundam. 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. Is there a unique invariant measure on X maximizing the weighted entropy h(X) h1 (Y ). J. Almeida, RIMS Kokyuroku 1366, 1 (2004). X is an irreducible subshift of finite type. ![]() Almeida, Finite Semigroups and Universal Algebra ( World Scientific, Singapore, 1995 ). (SFT) of positive entropy are isomorphic but they have some order structure. Let 6 be a finite alphabet, and let S be the shift on the shift space. 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. of an irreducible subshift of finite type into the FibonacciDyck shift. Finally we consider an analogous version of the problem for packing measure. Expansive actions with specification of sofic groups, strong. arise from geometric considerations involving the Rauzy graphs of the subshift. A subshift satisfying condition (b) (equivalently, condition (a)) in Proposition 2.10 is called strongly irreducible (cf. We also give applications of our results concerning Ahlfors regularity. in a natural way a profinite group to each irreducible subshift. For example, it fails in general for self-conformal sets, self-affine sets and Julia sets. An important class of subshifts consists of the irreducible shifts: Definition 10 A subshift X is irreducible (aka. 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. 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. 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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