Cohomology of GL(2,R)-valued cocycles over hyperbolic systems
Cohomology of GL(2,R)-valued cocycles over hyperbolic systems
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双曲系统上 GL(2,R) 值余循环的上同调
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发表时间：
2010
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通讯作者：
V. Sadovskaya
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作者：
V. Sadovskaya
考虑传递Anosov微分同态上的Holder连续GL（2，R）值环。给出了具有一个Lyapunov指数的环和保留两个横向Holder连续子束的环的Holder上同调的完全分类。证明了两个这样的环之间的可测上同调是Holder连续的。我们也证明了周期数据的共轭性对于两个这样的环并不总是意味着上同调，但是一个稍微强一点的假设可以。我们描述了一些例子，表明我们的主要结果不能推广到一般的GL（2，R）值环。
We consider Holder continuous GL(2,R)-valued cocycles over a transitive Anosov diffeomorphism. We give a complete classification up to Holder cohomology of cocycles with one Lyapunov exponent and of cocycles that preserve two transverse Holder continuous sub-bundles. We prove that a measurable cohomology between two such cocycles is Holder continuous. We also show that conjugacy of periodic data for two such cocycles does not always imply cohomology, but a slightly stronger assumption does. We describe examples that indicate that our main results do not extend to general GL(2,R)-valued cocycles.