平均跟踪性质与完全传递

The average-shadowing property and ergodicity

Blank在研究混沌动力学时,提出了平均跟踪性质的概念,本文将这一性质拓展到紧致度量空间.设X是紧致度量空间,f:X→X为同胚.本文主要证明:若f具有平均跟踪性质且是Lyapunov稳定的,则f是完全传递的,但它不是拓扑弱混合.

While researching chaotic dynamics, Blank has introduced the average-shadowing property. We extend the property to compact metric space. Let X is a compact metric space, f:X→X is a homoeomorphism. We prove that if f is Lyapunov stable with the average-shadowing property, it is totally transitive, but not topologically weakly mixing.