随机共形动力系统
Random conformal dynamical systems
摘要：
我们考虑随机动力系统，如群的共形变换与概率测度，或transversally共形叶理与拉普拉斯算子沿叶，在这种情况下，我们考虑holonomy伪群。我们证明，要么存在一个测量不变下的所有元素的组（或伪组），或几乎肯定是一个长的组合地图指数合同球。我们推出了一些关于唯一遍历性的结果。
英文摘要：
We consider random dynamical systems such as groups of conformal transformations with a probability measure, or transversaly conformal foliations with a Laplace operator along the leaves, in which case we consider the holonomy pseudo-group. We prove that either there exists a measure invariant under all the elements of the group (or the pseudo-group), or almost surely a long composition of maps contracts exponentially a ball. We deduce some results about the unique ergodicity.
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