论文标题
稳定的Lyapunov指数的刚度和Anosov地图的集成性
Rigidity of stable Lyapunov exponents and integrability for Anosov maps
论文作者
论文摘要
令$ f $是$ d $ -torus上的不可简化的不可约束的Anosov地图。我们表明，如果$ f $的稳定捆绑包是一维的，那么$ f $具有可集成的不稳定捆绑包，并且仅当且仅当每个周期点$ f $的每个周期点都以线性化的稳定捆绑包上同样的Lyapunov指数。对于高维稳定的捆绑包案例，我们在假设$ f $是线性anosov地图上具有真正简单的Lyapunov Spectrum在稳定的捆绑包上的线性Anosov地图的假设获得了相同的结果。在这两种情况下，这都意味着$ f $在拓扑上是与其线性化的拓扑结合，那么稳定捆绑包上的结合度平稳。
Let $f$ be a non-invertible irreducible Anosov map on $d$-torus. We show that if the stable bundle of $f$ is one-dimensional, then $f$ has the integrable unstable bundle, if and only if, every periodic point of $f$ admits the same Lyapunov exponent on the stable bundle with its linearization. For higher-dimensional stable bundle case, we get the same result on the assumption that $f$ is a $C^1$-perturbation of a linear Anosov map with real simple Lyapunov spectrum on the stable bundle. In both cases, this implies if $f$ is topologically conjugate to its linearization, then the conjugacy is smooth on the stable bundle.
