平移流的扭曲上同调方程
Twisted cohomological equations for translation flows
AI总结：
通过调和分析证明扭曲上同调方程解的存在性，导数损失至多3+，进而证明乘积平移流及时间-τ映射的稳定性。
摘要：
我们通过调和分析方法证明了在平移曲面上扭曲上同调方程解的存在性，其导数损失在Sobolev空间中至多为3+。作为推论，我们证明了在（三维）平移流形上的乘积平移流——即（高亏格）平移曲面与（平坦）圆的乘积——在A. Katok意义下是稳定的。进而，我们的乘积流结果蕴含了平移曲面上平移流的时间-τ映射的稳定性结果。
英文摘要：
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-τ maps of translation flows on translation surfaces.
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