论文标题
在部分双曲系统上的差异性旋转
Diffeomorphism cocycles over partially hyperbolic systems
论文作者
论文摘要
我们认为，在一个可访问的部分双曲系统上，Hölder的连续共生在紧凑型歧管$ M $的差异性中具有值。我们为此设置获得了几个结果。如果cocycle以$ c^{1+γ} $界定，我们表明它具有$γ$-Hölderriemannian riemannian liemannian在$ m $上的连续不变家族。我们建立了两个同伴之间可测量的结合性的连续性，假设两者都有束或固体的存在，并且在其中一个$ c^0 $中为$ c^0 $中的结合性。我们给出了两个共同体在循环重量方面存在连续共轭的条件。我们还研究了共同体的共轭和圣经之间的关系。我们的结果使沿纤维的偶联性定期丧失了，与固体和共生相比。
We consider Hölder continuous cocycles over an accessible partially hyperbolic system with values in the group of diffeomorphisms of a compact manifold $M$. We obtain several results for this setting. If a cocycle is bounded in $C^{1+γ}$, we show that it has a continuous invariant family of $γ$-Hölder Riemannian metrics on $M$. We establish continuity of a measurable conjugacy between two cocycles assuming bunching or existence of holonomies for both and pre-compactness in $C^0$ for one of them. We give conditions for existence of a continuous conjugacy between two cocycles in terms of their cycle weights. We also study the relation between the conjugacy and holonomies of the cocycles. Our results give arbitrarily small loss of regularity of the conjugacy along the fiber compared to that of the holonomies and of the cocycle.
