Subshifts of quasi-finite type

Abstract

We introduce subshifts of quasi-finite type as a generalization of the well-known subshifts of finite type. This generalization is much less rigid and therefore contains the symbolic dynamics of many non-uniform systems, e.g., piecewise monotonic maps of the interval with positive entropy. Yet many properties remain: existence of finitely many ergodic invariant probabilities of maximum entropy; lots of periodic points; meromorphic extension of the Artin-Mazur zeta function.

added examples, more precise estimates on periodic points and classification

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• On subshifts with slow forbidden word growth
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• Topological entropy of the set of generic points for $(\alpha -\beta )$-shifts
• A classification of intrinsic ergodicity for recognisable random substitution systems
• Ergodic optimization for continuous functions on non-Markov shifts