Mean sensitive, mean equicontinuous and almost periodic functions for dynamical systems


We show that an RdR^d-topological dynamical system equipped with an invariant ergodic measure has discrete spectrum if and only it is μ\mu-mean equicontinuous (proven for ZdZ^d before). In order to do this we introduce mean equicontinuity and mean sensitivity with respect to a function. We study this notion in the topological and measure theoretic setting. In the measure theoretic case we characterize almost periodic functions and in the topological case we show that weakly almost periodic functions are mean equicontinuous (the converse does not hold)

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    Last time updated on 08/12/2020