Quantitative mixing for locally Hamiltonian flows with saddle loops on compact surfaces

Given a compact surface $\mathcal{M}$ with a smooth area form $ω$, we consider an open and dense subset of the set of smooth closed 1-forms on $\mathcal{M}$ with isolated zeros which admit at least one saddle loop homologous to zero and we prove that almost every element in the former induces a mixing flow on each minimal component. Moreover, we provide an estimate of the speed of the decay of correlations for smooth functions with compact support on the complement of the set of singularities. T...