论文标题
随机双曲动力学的统计稳定性和线性响应
Statistical stability and linear response for random hyperbolic dynamics
论文作者
论文摘要
我们考虑了与Anosov差异的随机产物的家族，并表明对等效性和固定措施的相关家族的统计稳定性和线性响应具有。我们的分析依赖于参数化转移操作员共生的顶部oseledets空间以及临时抽象扰动语句的研究。作为一种应用，我们表明，当淬灭的中心极限定理在确保我们的共生响应的条件下，CLT的方差取决于参数。
We consider families of random products of close-by Anosov diffeomorphisms, and show that statistical stability and linear response hold for the associated families of equivariant and stationary measures. Our analysis rely on the study of the top Oseledets space of a parametrized transfer operator cocycle, as well as ad-hoc abstract perturbation statements. As an application, we show that, when the quenched central limit theorem holds, under the conditions that ensure linear response for our cocycle, the variance in the CLT depends differentiably on the parameter.
