English

Twisted cohomological equations for translation flows

Dynamical Systems 2023-06-22 v1

Abstract

We prove by methods of harmonic analysis a result on existence of solutions for twisted cohomological equations on translation surfaces with loss of derivatives at most 3+ in Sobolev spaces. As a consequence we prove that product translation flows on (3-dimensional) translation manifolds which are products of a (higher genus) translation surface with a (flat) circle are stable in the sense of A. Katok. In turn, our result on product flows implies a stability result of time-{\tau} maps of translation flows on translation surfaces.

Keywords

Cite

@article{arxiv.2007.04084,
  title  = {Twisted cohomological equations for translation flows},
  author = {Giovanni Forni},
  journal= {arXiv preprint arXiv:2007.04084},
  year   = {2023}
}

Comments

30 pages. arXiv admin note: text overlap with arXiv:0707.0940

R2 v1 2026-06-23T16:56:59.309Z