Academy of Mathematics and Systems Science, CAS Colloquia & Seminars

Speaker:

Prof. Yunping Jiang，The City University of New York and NSF，USA

Inviter:

Title:

Order of Oscillating Sequences, MMA-MMLS, and Sarnak's Conjecture

Time & Venue:

2018.7.17 16:00-17:00 N913

Abstract:

In this talk, I will explain several concepts, a log-uniformly oscillation sequence, an oscillation sequence, an oscillation sequence of higher order, a minimal mean attractable (MMA) dynamical system, a minimal mean-L-stable (MMLS) dynamical system. Equicontinuous dynamical systems are clearly MLS. Feigenbaum dynamical systems are not equicontinuous globally but when they are restricted on minimal sets still equicontinuous. Furthermore, in this talk I will give two non-trivial examples of dynamical systems which are not equicontinuous even when they are restricted on minimal sets but MMLS. We will prove that any oscillating sequence is linearly disjoint with all MMA and MMLS dynamical systems. One of the consequences is that Sarnak’s conjecture holds for all MMA and MMLS dynamical systems. There are dynamical systems which are not MMLS. Therefore, we need to use the concept of an oscillation sequence of higher order. The Mobius sequence is an example of an oscillation sequence of higher order due to a result of Hua. In this talk, I will give another interesting example of an oscillation sequence of higher order. Furthermore, I will prove that any oscillation sequence of order $d\geq 2$ is linearly disjoint with all affine distal maps of the $d$-torus.