平稳测度的光滑性

摘要：

研究了平稳测度关于迭代函数格式和定义它的权函数的光滑扰动的光滑性，主要定理将迭代函数格式和权函数的扰动的光滑性与平稳测度的扰动的光滑性联系起来.结果取决于平滑的迭代函数计划和权重函数;和空间上的固定措施作为一个线性算子。作为结果，我们还得到了极限集的豪斯多夫维数和平稳测度的豪斯多夫维数的光滑性.

英文摘要：

We study the smoothness of the stationary measure with respect to smooth perturbations of the iterated function scheme and the weight functions that define it. Our main theorems relate the smoothness of the perturbation of: the iterated function scheme and the weight functions; to the smoothness of the perturbation of the stationary measure. The results depend on the smoothness of: the iterated function scheme and the weights functions; and the space on which the stationary measure acts as a linear operator. As a consequence we also obtain the smoothness of the Hausdorff dimension of the limit set and of the Hausdorff dimension of the stationary measure.

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