Dendrite上的一些动力学性质
发布时间：2019-04-02 05:13
【摘要】：近年来,许多学者研究了dendrite上的动力系统性质,例如等度连续性、分离指数、轨道的收敛性、dendrite映射的极小集和中心深度等,但是dendrite上的等度连续性和中心深度尚有研究的空间.因此本文主要针对这两个方面对dendrite展开研究.一个连续统是一个非空紧致连通的度量空间,而一个局部连通的不包含闭合曲线的连续统叫做dendrite.本文主要有以下结果.在第三章中,设D是一个有有限个分支点的dendrite以及f是D到它自身的连续映射.用R(f)和P(f)来分别表示回归点集和非游荡点集.设Ωo(f)=D,Ωn(f)=Ω(f|Ω-1(f))(对任意的n∈N).满足Ωm(f)= Ωm+1(f)的最小的m ∈N ∪{∞}称为f的深度.在本文中,证明了Ω3(f)=R(f)以及f的深度不超过3.而且找到了一个dendrite T,使其有两个分支点,以及找到f是T到它自身的连续映射,使得Ω3(f)=R(f)≠Ω2(f).在第四章中,设T是一个有有限个分支点的dendrite以及f是T到它自身的连续映射.用ω(χ,f)表示在f作用下的ω-极限集.非游荡点集为Ω(χ,f)=.{存在点列{xk}(?)T以及递增序列{nk}(?) N,使得且对dendrite上的等度连续性进行研究,可得到如下等价结论：(1)f是等度连续的；(2)对任意的x∈T,ω(x,f)=Ω(x,f)；(3)对任意的x∈T,Ω(x,f)都是一条周期轨；(4)∩∞n=1fn(T)=P(f),并且对任意的x∈T,都有Card(ω(x,f))∞以及函数h:x →ω(x,f)(x∈f)连续.另外,还构造并证明了其他两个特殊的dendrite:(1)存在一个dendrite D和f是D到D的连续映射,使得P(f)=Ω(f)≠D=CR(f),并且对任意的n ∈N, fn无湍流.(2)存在一个dendrite D和f是D到D的连续映射,满足对某个的x∈D,存在y∈D,使得当x∈Sα(y,f)时,x (?) Sα(x,f).
[Abstract]:In recent years, many scholars have studied the properties of dynamical systems on dendrite, such as equal continuity, separation index, convergence of orbits, minimal sets of dendrite maps and central depth, etc. However, there is still room for research on equal continuity and central depth on dendrite. Therefore, this paper mainly focuses on these two aspects of the dendrite research. A continuum is a nonempty compact connected metric space, and a locally connected continuum without closed curves is called dendrite. The main results of this paper are as follows. In chapter 3, let D be a dendrite with finite fulcrum and f be a continuous mapping from D to itself. R (f) and P (f) are used to represent the regression point set and the non-wandering point set respectively. Let 惟 o (f) = D, 惟 n (f) = 惟 (f | 惟-1 (f) (). The minimum m 鈭，
本文编号：2452280
[Abstract]:In recent years, many scholars have studied the properties of dynamical systems on dendrite, such as equal continuity, separation index, convergence of orbits, minimal sets of dendrite maps and central depth, etc. However, there is still room for research on equal continuity and central depth on dendrite. Therefore, this paper mainly focuses on these two aspects of the dendrite research. A continuum is a nonempty compact connected metric space, and a locally connected continuum without closed curves is called dendrite. The main results of this paper are as follows. In chapter 3, let D be a dendrite with finite fulcrum and f be a continuous mapping from D to itself. R (f) and P (f) are used to represent the regression point set and the non-wandering point set respectively. Let 惟 o (f) = D, 惟 n (f) = 惟 (f | 惟-1 (f) (). The minimum m 鈭，
本文编号：2452280
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