一维动力系统是动力系统的一个重要组成部分，我们将结合复动力系统的方法，对含有wild attractor的区间映射展开一系列的研究，包括：wild attractor 的存在性、随机稳定性等问题。本项目的创新之处在于，运用principal nest 等组合工具寻找与以往不同的新的含有wild attractor 区间映射的例子，为wild attractor添加新的性质，同时注重复动力系统工具在区间映射中的应用。本课题的研究结果将丰富区间映射组合性质，为进一步的研究提供思路。

One dimension dynamics is an important part of dynamical systems。We will consider the interval maps with wild attractors combining the methods in complex dynamical systems。It includes the existence and stochastic stability of interval maps with wild attractors。The innovation of this item is that we will use principal nest to find new examples of interval maps with wild attractors，and add new properties for wild attractors。We will pay attention to the methods of complex dynamical systems。The results of this item will enrich the combinatorial properties of interval maps，and supply ideas for further study。