The chain relation in sofic subshifts

The paper gives a characterisation of the chain relation of a sofic subshift. Every sofic subshift $\Sigma$ can be described by a labelled graph $G$. Factorising $G$ in a suitable way we obtain the graph $G/_\approx$ that offers insight into some properties of the original subshift. Using $G/_\approx$ we describe first the chain relation in $\Sigma$, then characterise chain-transitive sofic subshifts, chain-mixing sofic subshifts and finally the attractors of the subshift dynamic system. At the end we present (straightforward) algorithms deciding chain-transitivity and chain-mixing properties of a sofic subshift and listing all the attractors of the subshift system.Comment: 14 pages, 9 figures, preprint (final version published in Fundamenta Informaticae

Characterizations of \omega-Limit Sets of Topologically Hyperbolic Systems

It is well known that \omega-limit sets are internally chain transitive and have weak incompressibility; the converse is not generally true, in either case. However, it has been shown that a set is weakly incompressible if and only if it is an abstract \omega-limit set, and separately that in shifts of finite type, a set is internally chain transitive if and only if it is a (regular) \omega-limit set. In this paper we generalise these and other results, proving that the characterization for shifts of finite type holds in a variety of topologically hyperbolic systems (defined in terms of expansive and shadowing properties), and also show that the notions of internal chain transitivity and weak incompressibility coincide in compact metric spaces.Comment: 15 pages. Author's affiliation updated in second version; main text unchange