Banach跟踪性质研究(英文)

On Banach Shadowing Property

设f是紧致度量空间X上的连续自映射。笔者引入一个新的跟踪性概念——Banach跟踪性质,讨论了Banach跟踪性质一些基本性质。主要证明了:Banach跟踪性质在迭代下被保持;如果f有Banach跟踪性质,那么它的链回复集、非游荡集和测度中心一致而且它的自然扩充也有Banach跟踪性质。

Let f be a continuous map from a compact metric space X to itself. In this paper, a new notion, the Banach shadowing property, is introduced. We initiate some basic discussions on it and show that Banach shadowing property is preserved under iterations. Among other things, it is shown that if f has Banach shadowing property, then chain recurrent set, nonwandering set and measure center of f coincide and the natural extension of f also has Banach shadowing property.