Nonsmooth one-dimensional maps: some basic concepts and definitions
Nonsmooth one-dimensional maps: some basic concepts and definitions
复制标题
DOI：
10.1080/10236198.2016.1248426
复制
发表时间：
2016-10
影响因子：
1.1
通讯作者：
I. Sushko;L. Gardini;V. Avrutin
中科院分区：
文献类型：
--
作者：
I. Sushko;L. Gardini;V. Avrutin
本综述的主要目的是为一维分段单调映射定义的动力系统理论做出贡献。我们回顾平滑映射理论中已知的一些定义，这些定义适用于分段平滑映射，并讨论特定于所考虑的映射类别的概念。为了让其他领域（尤其是应用领域）的研究人员能够清楚地了解演示内容，提供了许多示例。我们主要关注用于研究地图的各种吸引子以及在其参数空间中观察到的相关分叉结构的概念和概念。
The main purpose of the present survey is to contribute to the theory of dynamical systems defined by one-dimensional piecewise monotone maps. We recall some definitions known from the theory of smooth maps, which are applicable to piecewise smooth ones, and discuss the notions specific for the considered class of maps. To keep the presentation clear for the researchers working in other fields, especially in applications, many examples are provided. We focus mainly on the notions and concepts which are used for the investigation of various kinds of attractors of a map and related bifurcation structures observed in its parameter space.