Multiple recurrence without commutativity
| Autor: | Huang, Wen, Shao, Song, Ye, Xiangdong |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study multiple recurrence without commutativity in this paper. We show that for any two homeomorphisms $T,S: X\rightarrow X$ with $(X,T)$ and $(X,S)$ being minimal, there is a residual subset $X_0$ of $X$ such that for any $x\in X_0$ and any nonlinear integral polynomials $p_1,\ldots, p_d$ vanishing at $0$, there is some subsequence $\{n_i\}$ of $\mathbb Z$ with $n_i\to \infty$ satisfying $$ S^{n_i}x\to x,\ T^{p_1(n_i)}x\to x, \ldots,\ T^{p_d(n_i)}x\to x,\ i\to\infty.$$ Comment: 40 pages. arXiv admin note: text overlap with arXiv:2301.07873; text overlap with arXiv:2405.11251 by other authors |
| Databáze: | arXiv |
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