论文标题
分段线性迭代功能系统的特殊系列
Special families of piecewise linear iterated function systems
论文作者
论文摘要
本文研究了连续分段线性迭代函数系统的一些家庭的维度理论。对于一个家庭，我们表明，吸引子的Hausdorff尺寸等于从最自然的覆盖系统获得的指数增长率。我们还证明，对于Lebesgue典型参数，如果该数字大于1，并且所有收缩比为正，则基础吸引子的一维Lebesgue度量为正。
This paper investigates the dimension theory of some families of continuous piecewise linear iterated function systems. For one family, we show that the Hausdorff dimension of the attractor is equal to the exponential growth rate obtained from the most natural covering system. We also prove that for Lebesgue typical parameters, the 1-dimensional Lebesgue measure of the underlying attractor is positive, if this number is bigger than 1 and all the contraction ratios are positive.
