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We prove that minimal area-preserving flows locally given by a smooth Hamiltonian on a closed surface of genus g ≥ 2 are typically (in the measure-theoretical sense) not mixing. The result is obtained by considering special flows over interval exchange transformations under roof functions with symmetric logarithmic singularities and proving absence of mixing for a full measure set of interval exchange transformations. 1 The notion of typical here is measure-theoretical; i.e., it refers todoi:10.4007/annals.2011.173.3.10 fatcat:jslttrwac5bvbaoo236hk32hnm