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arXiv · 1511.05022

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

Aihua Fan·Yunping Jiang
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Abstract

We define oscillating sequences which include the M\"obius 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 M\"obius 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.

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Aihua Fan, Yunping Jiang. 2015-11-16. Oscillating Sequences, Minimal Mean Attractability and Minimal Mean-Lyapunov-Stability. https://doi.org/10.1017/etds.2016.121

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