强分离条件下弱自相似集的Hausdorff维数估计

Estimation of the Hausdorff dimension of a weak self-similar set under the strong separation condition

在强分离条件下研究由弱压缩系确定的弱自相似集的Hausdorff维数,利用质量分布原理得到了它的一个下界。结果表明,弱自相似集的Hausdorff维数的下界与压缩映射的不变集的Hausdorff维数的下界本质上是一致的。

The Hausdorff dimension of a weak self-similar set determined by a system of weak contractions is studied with the strong separation condition. Using the mass distribution principle, the lower bound for the Hausdorff dimension is got. It shows that the lower bound for the Hausdorff dimension of a weak self-similar set is essentially the same as that of the invariant set of contractions mapping.