Zero Entropy Interval Maps And MMLS-MMA Property

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 Möbius 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.

12 pages

References in corpus (1)

• Mean equicontinuity and mean sensitivity

Cited by in corpus (2)

• Mobius disjointness conjecture for local dendrite maps
• On dynamics of graph maps with zero topological entropy