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arXiv · 2007.04084

Twisted cohomological equations for translation flows

Giovanni Forni
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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.

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Giovanni Forni. 2020-07-06. Twisted cohomological equations for translation flows. https://doi.org/10.1017/etds.2021.120

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