An example of a weakly mixing BV vector field which is not strongly mixing

2022/08/25 by Zizza, Martina
#35Q35 #37A25 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.12174

Abstract

We give an example of a weakly mixing vector field b∈ L^∞([0,1],BV(\mathbbT²)) which is not strongly mixing. The example is based on a work of Chacon who constructed a weakly mixing automorphism which is not strongly mixing on ([0,1],B([0,1]),|⋅|), where B([0,1]) are the Borel subsets of [0,1] and |⋅| is the one-dimensional Lebesgue measure.

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