This paper is concerned with chaoti cation of discrete dynamical systems in nite-dimensional real spaces, via feedback control techniques. A chaoti cation theorem for one-dimensional discrete dynamical systems and a chaoti cation theorem for general higher-dimensional discrete dynamical systems are established, respectively. The controlled systems are proved to be chaotic in the sense of Devaney. In particular, the maps corresponding to the original systems and designed controllers are only required to satisfy some mild assumptions on two very small disjoint closed subsets in the domains of interest. This condition is weaker than those in the existing relevant literature.

This paper is concerned with chaos of discrete dynamical systems in complete metric spaces. Discrete dynamical systems governed by continuous maps in general complete metric spaces are first discussed, and two criteria of chaos are then established. As a special case, two corresponding criteria of chaos for discrete dynamical systems in compact subsets of metric spaces are obtained. These results have extended and improved the existing relevant results of chaos in finite-dimensional Euclidean spaces.

研究Banachl空间上连续Frechet可微映射导出的离散动力系统之混沌。建立一个由正则非退化同宿轨道产生混沌的判定定理，并对n维实空间上的离散动力系统的混沌进行了讨论，建立了两个由非退化返回扩张不动点产生混沌的判定定理，其中一个为Marotto定理的修正定理。特别地，分别给出了一般Banach空间及n维实空间上的连续可微映射不动点为扩张的充分必要条件，彻底解决了多年以来人们对n维实空间上连续可微映射不动点的扩张性与其Jacobi矩阵特征值之间关系的困惑。