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Twisted cohomological equations for translation flows

Published online by Cambridge University Press:  22 October 2021

GIOVANNI FORNI*
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD, USA

Abstract

We prove by methods of harmonic analysis a result on the 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 (three-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.

Type
Original Article
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

Dedicated to Anatole Katok, who taught us how to think

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