Ergodic averages for commutative transformations along return times
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911475227951104 |
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| author | Donoso, Sebastián Mondal, Sovanlal Saavedra-Araya, Vicente |
| author_facet | Donoso, Sebastián Mondal, Sovanlal Saavedra-Araya, Vicente |
| contents | In this paper, we extend recent results on the convergence of ergodic averages along sequences generated by return times to shrinking targets in rapidly mixing systems, partially answering questions posed by the first author, Maass and the third author. In particular, for a fixed parameter $a\in (0,1)$ and for generic $y\in [0,1]$, we establish both $L^2$ and pointwise convergence for single averages and multiple averages for commuting transformations along the sequences $(a_n(y))_{n\in \mathbb{N}}$, obtained by arranging the set $$\Big\{n\in\mathbb{N}: 0<2^ny \mod{1}<n^{-a} \Big\}$$ in an increasing order. We also obtain new results for semi-random ergodic averages along sequences of similar type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16188 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ergodic averages for commutative transformations along return times Donoso, Sebastián Mondal, Sovanlal Saavedra-Araya, Vicente Dynamical Systems Probability In this paper, we extend recent results on the convergence of ergodic averages along sequences generated by return times to shrinking targets in rapidly mixing systems, partially answering questions posed by the first author, Maass and the third author. In particular, for a fixed parameter $a\in (0,1)$ and for generic $y\in [0,1]$, we establish both $L^2$ and pointwise convergence for single averages and multiple averages for commuting transformations along the sequences $(a_n(y))_{n\in \mathbb{N}}$, obtained by arranging the set $$\Big\{n\in\mathbb{N}: 0<2^ny \mod{1}<n^{-a} \Big\}$$ in an increasing order. We also obtain new results for semi-random ergodic averages along sequences of similar type. |
| title | Ergodic averages for commutative transformations along return times |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2601.16188 |