不变集的一致完全性

Uniformly perfectness of attractors.

讨论R上一双李普希茨,C1+α映射有限族的不变集(吸引子)的性质.通过证明一个估计引理,证明了其不变集是一致完全集或单点集,作为一个应用,证明了当其不是单点集时,其Hausdorff维数大于零.

The properties of the attractor for a finite family of bi-Lipschitz and \$C^(1+α)\$ contractive maps on R are discussed. With an estimation lemma, it is proved that the attractor must be a perfect set or a single-point set. As an application, when the attractor isn't a single-point set, its Hausdorff dimension is positive.