半动力系统中闭集的稳定性和极限集映射的连续性

摘要

In this paper, we first discuss the relationships between the stabilities of closed sets in a given semidynamical system. Then we investigated the close relationships between the stability of limit sets, a kind of special closed sets in a semidynamical system, and the continuity of corresponding limit set maps. Furthermore, we give several necessary or sufficient conditions for the semicontinuity of some limit set maps.%研究了半动力系统中闭集的各种稳定性之间的关系和半动力系统中一类特殊的闭集即各种极限集的稳定性与相应极限集映射的半连续性之间的密切联系，给出了几个极限集映射上（下）半连续的充分或必要条件。