论文标题
双曲线动力学的Hölder-Zygmund空间中的径向源估计值
Radial source estimates in Hölder-Zygmund spaces for hyperbolic dynamics
论文作者
论文摘要
我们以Dyatlov-Zworski的精神证明了Hölder-Zygmund空间中的径向源估计值（也称为Anosov Flow）。主要结果是针对标记长度谱图的新的线性稳定性估计值，也称为Burns-Katok猜想。我们特别表明，在任何维度$ \ geq 2 $中，在否定的指标的空间中，$ c^{3+ \ varepsilon} $ - 具有相同长度频谱的关闭指标是等值的。这改善了Guillarmou-Knieper和第二作者的最新作品。 As a byproduct, this approach also allows to retrieve various regularity statements known in hyperbolic dynamics and usually based on Journé's lemma: the smooth Livšic Theorem of de La Llave-Marco-Moriyón, the smooth Livšic cocycle theorem of Niticā-Török for general (finite-dimensional) Lie groups, the rigidity of the regularity of the foliation obtained by Hasselblatt and 其他的。
We prove a radial source estimate in Hölder-Zygmund spaces for uniformly hyperbolic dynamics (also known as Anosov flows), in the spirit of Dyatlov-Zworski. The main consequence is a new linear stability estimate for the marked length spectrum rigidity conjecture, also known as the Burns-Katok conjecture. We show in particular that in any dimension $\geq 2$, in the space of negatively-curved metrics, $C^{3+\varepsilon}$-close metrics with same marked length spectrum are isometric. This improves recent works of Guillarmou-Knieper and the second author. As a byproduct, this approach also allows to retrieve various regularity statements known in hyperbolic dynamics and usually based on Journé's lemma: the smooth Livšic Theorem of de La Llave-Marco-Moriyón, the smooth Livšic cocycle theorem of Niticā-Török for general (finite-dimensional) Lie groups, the rigidity of the regularity of the foliation obtained by Hasselblatt and others.
