Orders of Oscillation Motivated by Sarnak's Conjecture--Part II

2022/01/21 by Yunping Jiang, Jiang, Yunping
Mathematics · #11K65 #11N05 #Advanced Mathematical Identities #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #Primary 37A35 #Secondary 37A25

paper · pdf · doi:10.48550/arxiv.2201.08800

openalex publication_date 2022/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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