巴拿赫空间上斜发展半流的离散渐近性
Discrete Asymptotic Behaviors for Skew-Evolution Semiflows on Banach Spaces
摘要：
本文着重讨论了由演化半流和演化上圈定义的斜演化半流的稳定性、不稳定性、二分法和半分性等渐近性质，这些性质可以看作是演化算子和斜积半流的推广.定义是在连续时间内给出的，但在离散时间内给出了非一致情形下所研究性质的统一刻画。S. Elaydi和O. Hajek于1988年提出的线性时变微分系统二分法的自然推广，我们分别从连续时间和一致时间的观点，以及离散时间和非一致时间的观点，但只对单参数半流的特殊情况进行了研究。
英文摘要：
The paper emphasizes asymptotic behaviors, as stability, instability, dichotomy and trichotomy for skew-evolution semiflows, defined by means of evolution semiflows and evolution cocycles and which can be considered generalizations for evolution operators and skew-product semiflows. The definition are given in continuous time, but the unified treatment for the characterization of the studied properties in the nonuniform case is given in discrete time. The property of trichotomy, introduced in finite dimension by S. Elaydi and O. Hajek in 1988 as a natural generalization for the dichotomy of linear time-varying differential systems, was studied by us in continuous time and from uniform point of view and in discrete time and from nonuniform point of view but for a particular case of one-parameter semiflows.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
