论文标题
双曲线摩托车自动形态的局部刚性
Local rigidity for hyperbolic toral automorphisms
论文作者
论文摘要
我们认为双曲线摩尔晶型$ l $及其$ c^1 $ -small扰动$ f $。众所周知，$ f $是Anosov，从拓扑结合到$ L $，但共轭$ H $通常是Hölder的一般。我们讨论了$ h $的平滑度的条件，例如$ f $和$ l $的定期数据的结合，其Lyapunov指数的巧合以及$ h $的规律性较弱，我们总结了该领域的问题，结果和技术。然后我们介绍了新的结果：如果$ h $是弱小的，那么它是$ c^{1+ \ text {hölder}} $，并且，如果$ l $也很弱，则$ h $是$ c^\ infty $。
We consider a hyperbolic toral automorphism $L$ and its $C^1$-small perturbation $f$. It is well-known that $f$ is Anosov and topologically conjugate to $L$, but a conjugacy $H$ is only Hölder continuous in general. We discuss conditions for smoothness of $H$, such as conjugacy of the periodic data of $f$ and $L$, coincidence of their Lyapunov exponents, and weaker regularity of $H$, and we summarize questions, results, and techniques in this area. Then we introduce our new results: if $H$ is weakly differentiable then it is $C^{1+\text{Hölder}}$ and, if $L$ is also weakly irreducible, then $H$ is $C^\infty$.
