Oscillating Sequences, Minimal Mean Attractability and Minimal Mean-Lyapunov-Stability

Abstract

We define oscillating sequences which include the Möbius function in the number theory. We also define minimally mean attractable flows and minimally mean-L-stable flows. It is proved that all oscillating sequences are linearly disjoint from minimally mean attractable and minimally mean-L-stable flows. In particular, that is the case for the Möbius function. Several minimally mean attractable and minimally mean-L-stable flows are examined. These flows include the ones defined by all $p$-adic polynomials, all $p$-adic rational maps with good reduction, all automorphisms of $2$-torus with zero topological entropy, all diagonalized affine maps of $2$-torus with zero topological entropy, all Feigenbaum zero topological entropy flows, and all orientation-preserving circle homeomorphisms.

43 pages, 4 figures

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