论文标题
$ C^1 $迭代功能系统和驱虫器的维度估算。第一部分
Dimension estimates for $C^1$ iterated function systems and repellers. Part I
论文作者
论文摘要
这是两部分系列中的第一篇文章，其中包含$ C^1 $迭代功能系统和驱虫剂的维度估计值的一些结果。在这一部分中，我们证明，$ {\ bbb r}^d $上任何$ C^1 $迭代功能系统（IFS）吸引子的上限计数尺寸上面是其奇异性维度，以及与此相关的任何与此相关的ERGODIC不变性措施的上层包装维度，如果与此相关联的lyapunov bious lyapunov diemension bious lyapunov diemension bious lyapunov diemension bious。对于$ C^1 $扩展了Riemannian歧管上的地图，驱虫者也获得了类似的结果。
This is the first article in a two-part series containing some results on dimension estimates for $C^1$ iterated function systems and repellers. In this part, we prove that the upper box-counting dimension of the attractor of any $C^1$ iterated function system (IFS) on ${\Bbb R}^d$ is bounded above by its singularity dimension, and the upper packing dimension of any ergodic invariant measure associated with this IFS is bounded above by its Lyapunov dimension. Similar results are obtained for the repellers for $C^1$ expanding maps on Riemannian manifolds.
