![]() If ∑ ⊆ AG is a strongly irreducible subshift of finite type, we endow a locally compact and Hausdorff topology on the homoclinic equivalence relation \( \right)\), G). Let G be an infinite countable group and A be a finite set. We also consider dual surjunctive systems for more general dynamical systems, namely for certain expansive algebraic actions, employing results of Chung and Li. View on Springer Save to Library Create Alert On the density of periodic configurations in strongly irreducible subshifts T. Moreover we show that dual surjunctive groups are closed under ultraproducts, under elementary equivalence, and under certain semidirect products (using the ideas of Arzhantseva and Gal for the latter) they form a closed subset in the space of marked groups, fully residually dual surjunctive groups are dual surjunctive, etc. 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. Fact.6 a) A is irreducible if and only if (XA,) is transitive. By quantifying the notions of injectivity and post-surjectivity for cellular automata, we show that the image of the full topological shift under an injective cellular automaton is a subshift of finite type in a quantitative way. Subshifts, Subshifts of Finite Type and Sofic Shifts. We show that dual surjunctive groups satisfy Kaplansky's direct finiteness conjecture for all fields of positive characteristic. For an irreducible subshift of finite type, the value of this measure on a basic cylinder set is easily. 350–359.We explore the dual version of Gottschalk's conjecture recently introduced by Capobianco, Kari, and Taati, and the notion of dual surjunctivity in general. 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. Weiss, B.: Sofic groups and dynamical systems, Sankhyā Ser. American Mathematical Society, Providence, RI (1988) Paterson A.L.T.: Amenability, Mathematical Surveys and Monographs, vol. Associated with these tilings there is a natural subshift of finite type, which is shown to be irreducible. Let Y be an irreducible subshift of finite type and let f : Y (0. The apartments of \\cB are tiled by triangles, labelled according to -orbits. about subshifts, the map will always be the shift map,, and it will be left implicit). Myhill J.: The converse of Moore’s Garden-of-Eden theorem. Let be a group of type rotating automorphisms of a building \\cB of type \\widetilde A2, and suppose that acts freely and transitively on the vertex set of \\cB. American Mathematical Society, Providence (1963) We also prove that if G is countable and X V G is a strongly irreducible linear subshift, then every injective linear cellular automaton : X X is surjective. Moore, E.F.: Machine models of self-reproduction, Proc. if X V G is a strongly irreducible linear subshift of nite type and : X X is a linear cellular automaton, then is surjective if and only if it is pre-injective. ![]() Cambridge University Press, Cambridge (1995) A necessary and sufficient condition is given for the existence of an embedding of an irreducible subshift of finite type into the FibonacciDyck shift. Lind D., Marcus B.: An introduction to symbolic dynamics and coding. Société Mathématique de France, Paris (2003) Kurka, P.: Topological and symbolic dynamics, Cours Spécialisés, vol. Hedlund G.A.: Endomorphisms and automorphisms of the shift dynamical system. Gromov M.: Endomorphisms of symbolic algebraic varieties. 16, Van Nostrand Reinhold Co., New York (1969) ![]() Greenleaf, F.P.: Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, vol. 11, 471–484 (2000)įiorenzi F.: Cellular automata and strongly irreducible shifts of finite type. We will say a subshift is irreducible if it has a dense forward orbit. Fourier (Grenoble) 49, 673–685 (1999)įiorenzi F.: The Garden of Eden theorem for sofic shifts. of finite type is almost Markov (Remark A.4), and the reducible shift of fi. 29, 371–380 (2009)Ĭeccherini-Silberstein T., Machì A., Scarabotti F.: Amenable groups and cellular automata. 26, 53–68 (2006)Ĭeccherini-Silberstein T., Coornaert M.: Induction and restriction of cellular automata. Ceccherini-Silberstein T., Coornaert M.: The Garden of Eden theorem for linear cellular automata. ![]()
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