Zero entropy continuous interval maps and MMLS-MMA property*This material is based upon work supported by the National Science Foundation. It is also partially supported by a collaboration grant from the Simons Foundation (grant number 523341) and PSC-CUNY awards and a grant from NSFC (grant number 11571122). (2nd May 2018)

• Record Type: Journal Article
• Authors: Jiang, Yunping
• Is Part Of: Nonlinearity. Volume 31:Number 6(2018:Jun.)
• Page Start: 2689
• Page End: 2702
• Publication Date: 2018-05-02
• Subjects: minimally mean-attractable (MMA) -- minimally mean-L-stable (MMLS) -- linear disjointness -- Mobius function -- oscillating sequence -- Sarnak's conjecture -- continuous interval map with zero topological entropy; Primary; 11K65 -- 37A35 -- Secondary; 37A25 -- 11N05; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aab593
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We prove that the flow generated by any continuous interval map with zero topological entropy is minimally mean-attractable and minimally mean-L-stable. One of the consequences is that any oscillating sequence is linearly disjoint from all flows generated by all continuous interval maps with zero topological entropy. In particular, the Möbius function is linearly disjoint from all flows generated by all continuous interval maps with zero topological entropy (Sarnak's conjecture for continuous interval maps). Another consequence is a non-trivial example of a flow having discrete spectrum. We also define a log-uniform oscillating sequence and show a result in ergodic theory for comparison.