Zero Entropy Interval Maps And MMLS-MMA Property
Dynamical Systems
2020-06-02 v1
Abstract
We prove that the flow generated by any interval map with zero topological entropy is minimally mean-attractable (MMA) and minimally mean-L-stable (MMLS). One of the consequences is that any oscillating sequence is linearly disjoint with all flows generated by interval maps with zero topological entropy. In particular, the M\"obius function is orthogonal to all flows generated by interval maps with zero topological entropy (Sarnak's conjecture for interval maps). Another consequence is a non-trivial example of a flow having the discrete spectrum.
Cite
@article{arxiv.1708.05755,
title = {Zero Entropy Interval Maps And MMLS-MMA Property},
author = {Yunping Jiang},
journal= {arXiv preprint arXiv:1708.05755},
year = {2020}
}
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12 pages