Radial source estimates in Hölder-Zygmund spaces for hyperbolic dynamics
Radial source estimates in Hölder-Zygmund spaces for hyperbolic dynamics
复制标题
双曲动力学 Hölder-Zygmund 空间中的径向源估计
DOI：
10.5802/ahl.175
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发表时间：
2020
影响因子：
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通讯作者：
Thibault Lefeuvre
中科院分区：
文献类型：
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作者：
Y. Bonthonneau;Thibault Lefeuvre
我们证明径向源估计在霍尔德-Zygmund空间的一致双曲动力学（也称为Anosov流），在Dyatlov-Zworski的精神。这种方法提供了一个统一的框架，各种正则性声明中已知的双曲动力学，如：光滑的利夫西奇定理的德拉Llave-马可-Moriyon，光滑的利夫西奇上循环定理的Nitichte-Torok一般（有限维）李群，刚性的正则性的叶理获得的Hasselblatt和其他人。这也意味着一个新的线性稳定性估计的标记长度谱猜想（也被称为伯恩斯-Katok猜想），这是独立的维度和改善最近的作品Guillarmou-Gilleper和第二作者。
We prove radial source estimates in Holder-Zygmund spaces for uniformly hyperbolic dynamics (also known as Anosov flows), in the spirit of Dyatlov-Zworski. This approach provides a unifying framework for various regularity statements known in hyperbolic dynamics such as: the smooth Livsic theorem of de La Llave-Marco-Moriyon, the smooth Livsic cocycle theorem of Niticā-Torok for general (finite-dimensional) Lie groups, the rigidity of the regularity of the foliation obtained by Hasselblatt and others. This also implies a new linear stability estimate for the marked length spectrum conjecture (also known as the Burns-Katok conjecture) which is independent of the dimension and improves recent works by Guillarmou-Knieper and the second author.