传递系统中的不变攀援集

摘要

The concept of scrambled sets is generalized and invariant scrambled sets in transitive systems are investigated. It is proved that under certain conditions, which include many usual cases, a transitive system admits a totally scrambled set that is a dense σ-Cantor subset of the space and is invariant under the map in consideration.%推广了攀援集的概念.研究了传递系统中的不变攀援集.证明了在相当广泛的条件下,一个传递系统有一个不变的稠密的σ-Cantor子集是完全攀援集.