迭代函数系统的吸引子

Attractors of iterated function system

研究了迭代函数系统的吸引子 .通过分析Rd 上迭代函数系统的吸引子的点的分布情况以及它与OSC集之间的关系 ,具体分析了R上由三个和多个相似变换组成的一类迭代函数系统吸引子的结构 .研究结果显示了迭代函数系统的吸引子的复杂性 ,对分形几何中关于研究分形集的某些性质 ,如豪斯多夫维数、测度等具有帮助作用 ,同时对小波分析、动力系统等其他方面的研究工作提供了依据和参考 .

By analyzing the distribution of the attractor points and the relation between the attractors and the OSC sets, the attractor structures of the iterated function system on R consisting of three or more similarities was analyzed. The result showed the complexity of the attractors of the iterated function system. It was helpful to study the properties of the fractal set, such as Hausdorff dimension, measure and so on. The result provided the basis for other researches, such as wavelet analysis and dynamical system.