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Singularity of the Spectrum for Smooth Area-Preserving Flows in Genus Two and Translation Surfaces Well Approximated by Cylinders
We consider smooth flows preserving a smooth invariant measure, or, equivalently, locally Hamiltonian flows on compact orientable surfaces and show that, when the genus of the surface is two, almost every such locally Hamiltonian flow with two non degenerate isomorphic saddle has singular spectrum. More in general, singularity of the …