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.
設(X, d1, f1,∞)與(Y, d2, g1,∞)為兩箇非自治動力繫統, h 是從(X, d1, f1,∞)到(Y, d2, g1,∞)的拓撲半共軛.通過對自治動力繫統中的 h-極小覆蓋的研究,本文得到瞭以下結論:1)對于任意的 y ∈ Y 及 x ∈ h?1(y), orb(x, f1,∞)被 h 映射為 orb(y, g1,∞),ω(x, f1,∞)被 h 映射為ω(y, g1,∞);2)在(X, d1, f1,∞)中引入關于拓撲半共軛的 h-極小覆蓋的定義,證明瞭 h-極小覆蓋的存在性;3)對于任意的 x∈X和y∈Y ,在(ω(x, f1,∞), f1,∞|ω(x,f1,∞))與(ω(y, g1,∞), g1,∞|ω(y,g1,∞))均構成原繫統的子繫統的前提下, R(f1,∞)被h 映射為R(g1,∞).這些結論豐富瞭非自治動力繫統的內容.
설(X, d1, f1,∞)여(Y, d2, g1,∞)위량개비자치동력계통, h 시종(X, d1, f1,∞)도(Y, d2, g1,∞)적탁복반공액.통과대자치동력계통중적 h-겁소복개적연구,본문득도료이하결론:1)대우임의적 y ∈ Y 급 x ∈ h?1(y), orb(x, f1,∞)피 h 영사위 orb(y, g1,∞),ω(x, f1,∞)피 h 영사위ω(y, g1,∞);2)재(X, d1, f1,∞)중인입관우탁복반공액적 h-겁소복개적정의,증명료 h-겁소복개적존재성;3)대우임의적 x∈X화y∈Y ,재(ω(x, f1,∞), f1,∞|ω(x,f1,∞))여(ω(y, g1,∞), g1,∞|ω(y,g1,∞))균구성원계통적자계통적전제하, R(f1,∞)피h 영사위R(g1,∞).저사결론봉부료비자치동력계통적내용.
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.
