关于定义在满足强分离条件的自相似集上的动力系统的一点注记(英文)

A Note on the Dynamical System Defined on A Self-similar Set Satisfying SSC

在满足强分离条件的自相似集上 ,可以定义一个连续自映射。这个自相似集的单位化的Hausdorff测度是它的不变遍历测度。

A classical result says, for a self-similar set satisfying the strong separation condition,one can define a continuous self-mapping on it with the normalized Hausdorff measure of the self-similar set as its invariant ergodic measure.A necessary and sufficient condition for the normalized Hausdorff measure to be a measure with maximal entropy for the self-mapping is given.