The recurrence spectrum for dynamical systems beyond specification
Abstract
Abstract We introduce (W′)-specification in terms of language decompositions of subshifts, and show that any recurrence set of a subshift with this property has full Hausdorff dimension. Our main result applies to a wide class of subshifts without specification, such as all S -gap shifts, some coded shifts, and the coding space of any transitive piecewise monotonic interval map with positive entropy. Further, for a wide class of piecewise expanding interval maps we show that any recurrence set has full Hausdorff dimension.
Fields of Study & Subjects
Cellular Automata and Applications
Mathematical Dynamics and Fractals
semigroups and automata theory
Publication details
- Journal / source
- Nonlinearity
- Volume
- 39
- Issue
- 4
- Pages
- 045014–045014
- Publication date
- 22 April 2026
- Language
- EN