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We prove that the flow generated by any interval map with zero topologicalentropy is minimally mean-attractable (MMA) and minimally mean-L-stable (MMLS).One of the consequences is that any oscillating sequence is linearly disjointwith all flows generated by interval maps with zero topological entropy. Inparticular, the M\"obius function is orthogonal to all flows generated byinterval maps with zero topological entropy (Sarnak's conjecture for intervalmaps). Another consequence is a non-trivial example of a flow having thediscrete spectrum.

Zero Entropy Interval Maps And MMLS-MMA Property