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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.19082 |
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| _version_ | 1866918165428043776 |
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| author | Folks, Jacob |
| author_facet | Folks, Jacob |
| contents | "Higher-order Wiener-Wintner averages" were constructed by Assani, Folks, and Moore to quantitatively control multiple recurrence averages. Systems in which these averages converge at a polynomial rate for a sufficiently large subset are termed "higher-order Wiener-Wintner systems of power type", in which properties like pointwise convergence of multiple recurrence averages and multiple return times averages has been shown. We establish that these higher-order Wiener-Wintner averages satisfy a type of sublinearity, and that they bound conditional expectations and products, which transfers to improved stability results of higher-order Wiener-Wintner systems under sums, factors, and products. We also establish more general convergence results for such systems, which include a polynomial return times theorem and convergence of the multilinear one-side ergodic Hilbert transform with polynomial phase. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19082 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | More stability and convergence results for higher-order Wiener-Wintner systems Folks, Jacob Dynamical Systems "Higher-order Wiener-Wintner averages" were constructed by Assani, Folks, and Moore to quantitatively control multiple recurrence averages. Systems in which these averages converge at a polynomial rate for a sufficiently large subset are termed "higher-order Wiener-Wintner systems of power type", in which properties like pointwise convergence of multiple recurrence averages and multiple return times averages has been shown. We establish that these higher-order Wiener-Wintner averages satisfy a type of sublinearity, and that they bound conditional expectations and products, which transfers to improved stability results of higher-order Wiener-Wintner systems under sums, factors, and products. We also establish more general convergence results for such systems, which include a polynomial return times theorem and convergence of the multilinear one-side ergodic Hilbert transform with polynomial phase. |
| title | More stability and convergence results for higher-order Wiener-Wintner systems |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2510.19082 |