连续流的渐近平均跟踪性质与传递性

The asymptotic average shadowing property and transitivity for continuous flows

对于连续流,引入渐近平均跟踪性质的概念,讨论了具有渐近平均跟踪性质的连续流与一些动力性质的关系.证明了具有渐近平均跟踪性质的连续流是链传递的,且具有渐近平均跟踪性质的Lyapunov稳定的连续流是一个极小流.

For continuous flows, the notion of the asymptotic average shadowing property was introduced and the relations between the asymptotic average shadowing property and some dynamical properties were investigated. It was shown that a continuous flow with asymptotic average shadowing property was chain transitive and a continuous Lyapunov stable flow with the asymptotic average shadowing property was a minimal flow.