关于中心间的不变整体性

Pub Date : 2024-05-08 DOI:10.1017/etds.2024.33

RADU SAGHIN

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引用次数: 0

摘要

我们证明，对于$C^{1+\theta }$ , $\theta $ -束状、动态相干的部分双曲衍射，中心叶之间的稳定和不稳定整体性为$C^1$，导数连续依赖于点和映射。同样对于 $C^{1+\theta }$ , $\theta $ 组合的部分双曲衍射，限制于中心束的导数环具有不变的连续整体性，这些整体性连续地依赖于映射。这概括了 Pugh、Shub 和 Wilkinson、Burns 和 Wilkinson、Brown、Obata、Avila、Santamaria 和 Viana 以及 Marin 以前的结果。

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On invariant holonomies between centers

We prove that for

$C^{1+\theta }$

$\theta $

-bunched, dynamically coherent partially hyperbolic diffeomorphisms, the stable and unstable holonomies between center leaves are

$C^1$

, and the derivative depends continuously on the points and on the map. Also for

$C^{1+\theta }$

$\theta $

-bunched partially hyperbolic diffeomorphisms, the derivative cocycle restricted to the center bundle has invariant continuous holonomies which depend continuously on the map. This generalizes previous results by Pugh, Shub, and Wilkinson; Burns and Wilkinson; Brown; Obata; Avila, Santamaria, and Viana; and Marin.

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