论文标题
特征指数的规律性和转移操作员共生的线性响应
Regularity of characteristic exponents and linear response for transfer operator cocycles
论文作者
论文摘要
我们考虑通过组合具有正权重的转移算子的序列，与统一扩展的地图（可能具有数量很多分支）相关，并取决于参数，获得的旋转序列。假设$ c^k $规律性相对于坐标和参数，我们表明，当序列在某个统一家族中选择序列时，cocycle的顶部oseledets空间的顶部特征指数和生成器是参数中的$ c^{k-1} $。作为应用，我们获得了与均匀扩展地图的随机产物相关的均值度量的线性响应公式，并且我们研究了与一维饼干曲线的随机组成相关的驱虫剂的Hausdorff维度的规律性。
We consider cocycles obtained by composing sequences of transfer operators with positive weights, associated with uniformly expanding maps (possibly having countably many branches) and depending upon parameters. Assuming $C^k$ regularity with respect to coordinates and parameters, we show that when the sequence is picked within a certain uniform family the top characteristic exponent and generator of top Oseledets space of the cocycle are $C^{k-1}$ in parameters. As applications, we obtain a linear response formula for the equivariant measure associated with random products of uniformly expanding maps, and we study the regularity of the Hausdorff dimension of a repeller associated with random compositions of one-dimensional cookie-cutters.
