论文标题
全球耦合的Anosov差异性：统计特性
Globally coupled Anosov diffeomorphisms: Statistical properties
论文作者
论文摘要
我们研究了偶联强度较弱的全球耦合Anosov差异的无限系统。使用在各向异性BANACH空间上作用的转移操作员，我们证明了耦合系统可以接受独特的物理不变状态，即$ H_ \ VAREPSILON $。此外，我们证明了适合一类分布类别的指数收敛到平衡，并表明地图$ \ varepsilon \ mapsto h_ \ varepsilon $是Lipschitz的连续。
We study infinite systems of globally coupled Anosov diffeomorphisms with weak coupling strength. Using transfer operators acting on anisotropic Banach spaces, we prove that the coupled system admits a unique physical invariant state, $h_\varepsilon$. Moreover, we prove exponential convergence to equilibrium for a suitable class of distributions and show that the map $\varepsilon\mapsto h_\varepsilon$ is Lipschitz continuous.
