Pointwise convergence in nilmanifolds along smooth functions of polynomial growth
| Autor: | Tsinas, Konstantinos |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Ergod. Th. Dynam. Sys. 44 (2024) 1963-2008 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/etds.2023.68 |
| Popis: | We study the equidistribution of orbits of the form $b_1^{a_1(n)}... b_k^{a_k(n)}\Gamma$ in a nilmanifold $X$, where the sequences $a_i(n)$ arise from smooth functions of polynomial growth belonging to a Hardy field. We show that under certain assumptions on the growth rates of the functions $a_1,...,a_k$, these orbits are uniformly distributed on some subnilmanifold of the space $X$. As an application of these results and in combination with the Host-Kra structure theorem for measure preserving systems, as well as some recent seminorm estimates of the author for ergodic averages concerning Hardy field functions, we deduce a norm convergence result for multiple ergodic averages. Our method mainly relies on an equidistribution result of Green-Tao on finite polynomial orbits of a nilmanifold. Comment: 34 pages, Several corrections, Referee suggestions incorporated, To appear in Ergodic Theory and Dynamical Systems |
| Databáze: | arXiv |
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