The recurrence spectrum for dynamical systems beyond specification
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911485378166784 |
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| author | Takahasi, Hiroki |
| author_facet | Takahasi, Hiroki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01485 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The recurrence spectrum for dynamical systems beyond specification Takahasi, Hiroki Dynamical Systems Number Theory 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. |
| title | The recurrence spectrum for dynamical systems beyond specification |
| topic | Dynamical Systems Number Theory |
| url | https://arxiv.org/abs/2509.01485 |