Orders of Oscillation Motivated by Sarnak's Conjecture--Part II
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909896849489920 |
|---|---|
| author | Jiang, Yunping |
| author_facet | Jiang, Yunping |
| contents | This work is a continuation of [13]. We study the linear disjointness between higher-order oscillating sequences and nonlinear dynamical systems. Specifically, we prove that any oscillating sequence of order $m=d+k-1$ and any simple polynomial skew product of degree $k$ on the $d$-Euclidean space are linearly disjoint. Additionally, we demonstrate that any oscillating sequence of order $d$ and any minimal mean attractable and minimal quasi-discrete spectrum dynamical system of order $d$ are linearly disjoint. Finally, we introduce multi-linearly disjoint sequences and construct examples of such sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_08800 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Orders of Oscillation Motivated by Sarnak's Conjecture--Part II Jiang, Yunping Dynamical Systems Number Theory Primary 37A35, 11K65, Secondary 37A25, 11N05 This work is a continuation of [13]. We study the linear disjointness between higher-order oscillating sequences and nonlinear dynamical systems. Specifically, we prove that any oscillating sequence of order $m=d+k-1$ and any simple polynomial skew product of degree $k$ on the $d$-Euclidean space are linearly disjoint. Additionally, we demonstrate that any oscillating sequence of order $d$ and any minimal mean attractable and minimal quasi-discrete spectrum dynamical system of order $d$ are linearly disjoint. Finally, we introduce multi-linearly disjoint sequences and construct examples of such sequences. |
| title | Orders of Oscillation Motivated by Sarnak's Conjecture--Part II |
| topic | Dynamical Systems Number Theory Primary 37A35, 11K65, Secondary 37A25, 11N05 |
| url | https://arxiv.org/abs/2201.08800 |