تقرير
Non-commuting transformations with non-converging 2-fold ergodic averages
| العنوان: | Non-commuting transformations with non-converging 2-fold ergodic averages |
|---|---|
| المؤلفون: | Ryzhikov, Valery V. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Dynamical Systems |
| الوصف: | In connection with the results of Tim Austin, and Wen Huang, Song Shao, Xiangdong Ye we present the following assertion: there are infinite automorphisms $S,T$, some set $A$ of positive finite measure and a sequence $N_m$ with $|N_{m+1}|/|N_m|\ \to\infty$ such that $T^iA\cap S^iA=\phi$ for $i\in [N_{4k}, N_{4k+1}]$ and $T^iA=S^iA$ for $i\in [N_{4k+2}, N_{2k+3}]$. For the corresponding deterministic Gaussian and Poisson suspensions $S_\circ,T_\circ$ over $S,T$ for some $f\in L_\infty$ there is not a limit of $ \frac 1 N \sum_{n=1}^N T_\circ^nf\,S_\circ^nf$ in $ L_2$. Comment: in English and Russian versions |
| نوع الوثيقة: | Working Paper |
| اللغة: | English |
| URL الوصول: | http://arxiv.org/abs/2407.13741 |
| رقم الأكسشن: | edsarx.2407.13741 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |