论文标题
真实和复杂的投影表面的随机动力学
Random dynamics on real and complex projective surfaces
论文作者
论文摘要
我们启动研究真实和复杂的射影表面自动形态的随机迭代，或更通常是紧凑的k {ä} hler表面，重点介绍了固定度量分类的基本问题。我们表明，在许多情况下，这种固定措施是不变的，并提供了不变概率度量的独特性，平滑性和刚性的标准。这涉及各种工具，包括复杂和代数几何形状，矩阵的随机产物，不均匀的双曲线，以及Brown和Rodriguez Hertz在表面差异的随机迭代中的最新结果。
We initiate the study of random iteration of automorphisms of real and complex projective surfaces, or more generally compact K{ä}hler surfaces, focusing on the fundamental problem of classification of stationary measures. We show that, in a number of cases, such stationary measures are invariant, and provide criteria for uniqueness, smoothness and rigidity of invariant probability measures. This involves a variety of tools from complex and algebraic geometry, random products of matrices, non-uniform hyperbolicity, as well as recent results of Brown and Rodriguez Hertz on random iteration of surface diffeomorphisms.
