English

Some real Rel trajectories in $\mathcal{H}(1,1)$ that are not recurrent

Dynamical Systems 2024-06-12 v1

Abstract

We study the real Rel orbits of some translation surfaces in the stratum H(1,1)\mathcal{H}(1,1). 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.

Keywords

Cite

@article{arxiv.2406.07495,
  title  = {Some real Rel trajectories in $\mathcal{H}(1,1)$ that are not recurrent},
  author = {Carlos Ospina},
  journal= {arXiv preprint arXiv:2406.07495},
  year   = {2024}
}

Comments

27 pages, 6 figures. Comments are welcome!