摘要：Let (X, d1, f1,∞) and (Y, d2, g1,∞) are non-autonomous discrete dynamical systems, (Y, d2, g1,∞) is quasiconjugate to (X, d1, f1,∞) via h : X → Y . By using the h-minimal covering of autonomous discrete dynamical systems, we can obtain the following resluts : 1) For any point y ∈ Y , x ∈ h−1(y), there are h(orb(x, f1,∞)) = orb(y, g1,∞) and h(ω(x, f1,∞)) = ω(y, g1,∞); 2) We define the h-minimal covering of non-autonomous discrete dynamical systems (X, d1, f1,∞). In addition, the existence of the h-minimal covering is studied; 3) For any point x∈X, y∈Y , while (ω(x, f1,∞), f1,∞|ω(x,f1,∞)) and (ω(y, g1,∞), g1,∞|ω(y,g1,∞)) are subsystems of the original systems, we have h(R(f1,∞))=R(g1,∞). These conclusions enriched the contents of non-autonomous discrete dynamical systems.% 设(X, d1, f1,∞)与(Y, d2, g1,∞)为两个非自治动力系统, h 是从(X, d1, f1,∞)到(Y, d2, g1,∞)的拓扑半共轭。通过对自治动力系统中的 h-极小覆盖的研究,本文得到了以下结论：1)对于任意的 y ∈ Y 及 x ∈ h−1(y), orb(x, f1,∞)被 h 映射为 orb(y, g1,∞),ω(x, f1,∞)被 h 映射为ω(y, g1,∞)；2)在(X, d1, f1,∞)中引入关于拓扑半共轭的 h-极小覆盖的定义,证明了 h-极小覆盖的存在性；3)对于任意的 x∈X和y∈Y ,在(ω(x, f1,∞), f1,∞|ω(x,f1,∞))与(ω(y, g1,∞), g1,∞|ω(y,g1,∞))均构成原系统的子系统的前提下, R(f1,∞)被h 映射为R(g1,∞)。这些结论丰富了非自治动力系统的内容。
