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arXiv · 2509.01485

The recurrence spectrum for dynamical systems beyond specification

Hiroki Takahasi
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Abstract

We introduce {\it (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.

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Hiroki Takahasi. 2025-09-01. The recurrence spectrum for dynamical systems beyond specification. https://arxiv.org/abs/2509.01485

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