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We show the existence of a dense orbit for real Rel flows on the area-1 locusof every connected component of every stratum of holomorphic 1-forms with atleast 2 distinct zeros. For this purpose, we establish a general densitycriterion for ${\rm SL}(2,\mathbb{R})$-orbit closures, based on finding anorbit of a real Rel flow whose closure contains a horocycle. This criterion canbe verified using explicit constructions of holomorphic 1-forms with a periodichorizontal foliation. Our constructions also provide explicit examples of denseleaves of the absolute period foliation and many subfoliations of these loci.

Dense real Rel flow orbits and absolute period leaves