Some real {Rel} trajectories in that are not recurrent
arXiv:2406.07495
Abstract
We study the real Rel orbits of certain translation surfaces in the stratum , specifically surfaces that are tremors of the locus of branched double covers of tori. We give necessary and sufficient conditions on tremors of a surface so that the real Rel orbit is recurrent. As a consequence, we are able to provide explicit examples of trajectories of real Rel that are not recurrent.
34 pages, 3 figures. Comments are welcome