单谷Feigenbaum映射的拟极限集

给出了单谷Feigenbaum映射拟极限集的结构以及它的准确的Hausdorff维数的关系式。     

非单谷的p阶Feigenbaum映射

The author considers the Feigenbaum's functional equation f^P(λx) = λf(x) for each p ≥ 2. The existence of nonsingle-valley continuous solutions to this equation is discussed and a feasible method to construct such solutions is given.     

两类Feigenbaum映射的拟极限集的Hausdorff测度

本计算了一类无穷多峰Feigenbaum映射一类单峰Feigenbaum映射的拟极限集的Hausdorff测度。     

两类Feigen baum映射的拟极限集的Hausdorff测度

本文计算了一类无穷多峰 Feigenbaum映射和一类单峰 Feigenbaum映射的拟极限集的Hausdorff测度     

分形拟极限集的可积性

本文讨论了螺线型拟极限集的可积性.作为应用,研究了Feigenbaum乘积映射的分 形拟极限集.     

拟共形映射和HAUSDORFF维数

讨论了标准Cantor集 F 的Hausdorff维数dim_H(F)在拟共形映射 f 下的变化, 给出了dim_H(f(F))的准确上下界.     

3阶Feigenbaum映射的拓扑共轭性

本文讨论3阶Feigenbaum映射限制在非游荡集上的拓扑共轭性．一方面3阶Feigenbaum映射必然产生混沌,混沌的产生使得非游荡集复杂化;另一方面3阶Feigenbaum映射又分为单谷的和非单谷的两类．利用有限型子转移,证明了对任意给定的两个满足一定条件的3阶Feigenbaum映射,限制在其非游荡集上是拓扑共轭．     

树映射的ω-极限集

Let T be a tree and f be a continuous map form T into itself.We show mainly in this paper that a point x of T is an ω-limit point of f if and only if every open neighborhood of x in T contains at least nx 1 points of some trajectory,where nx equals the number of connected components of T/{x}.Then,for any open subset Gω(f) in T,there exists a positive integer m=m(G) such that at most m points of any trajectory lie outside G.This result is a generalization of the related result for maps of the interval.     

Likely Limit Sets of a Class of p-order Feigenbaum's Maps

A continuous map from a closed interval into itself is called a p-order Feigenbaum's map if it is a solution of the Feigenbaum's equation fp(λx) =λf(x).In this paper,we estimate Hausdorff dimensions of...     

Likely Limit Sets of a Class of $p$-Order Feigenbaum's Maps

A continuous map from a closed interval into itself is called a $p$-order Feigenbaum's map if it is a solution of the Feigenbaum's equation $f^p (λx) = λf(x)$. In this paper, we estimate Hausdorff dimensions of likely limit sets of some $p$-order Feigenbaum's maps. As an application, it is proved that for any $0 < t < 1$, there always exists a $p$-order Feigenbaum's map which has a likely limit set with Hausdorff dimension $t$. This generalizes some known results in the special case of $p = 2$.     

Likely Limit Sets of Feigenbaum''''s Maps and Their Hausdorf f Dimensions

A continuous map from a closed interval into itself is called a Feigenbaum's map if it is a solution of the functional equation f2(λx)=λf(x).In this paper, the likely limit sets of a type of Feigenbaum's maps are studied and their Hausdorff dimensions are estimated.As an application, we prove that for any 0相似文献   

Fengenbaum映射的搓揉序列与特征集

设f为Feigenbaum映射,亦即函数方程fp(λx)=λf(x)满足一定条件的单峰解．f的搓揉序列为0-1无限序列,f的特征集是临界点轨迹的闭包．本文研究f的性质进而证明．f的搓揉序列是某代换在符号空间中的不动点,f在特征集上的限制是某代换子移位的一个因子．     

自相似集之间的等变映射

定义了复射动力系统以及它们之间等变映射的概念 ,在此基础上又引出了自相似集之间等变映射的概念并讨论了在此类映射的映射下自相似集象的 Hausdorff维数的状态 .     

Stable Stationary Harmonic Maps to Spheres

For k ≥ 3, we establish new estimate on Hausdorff dimensions of the singular set of stable-stationary harmonic maps to the sphere S^k. We show that the singular set of stable-stationary harmonic maps from B5 to 83 is the union of finitely many isolated singular points and finitely many HSlder continuous curves. We also discuss the minimization problem among continuous maps from B^n to S^2.     

Tyson型集及Borel函数的图的拟对称极小性

本文将欧氏空间R^d中形如[0,1]×Z的集称为Tyson型集,其中d>1,Z⊂R^d-1.已知当Z是R^d-1中的紧集时,Tyson型集是拟对称极小集.本文改进了这个结果,证明了当Z是R^d-1中的Borel集时,Tyson型集仍是拟对称极小集.作为应用,我们证明了Tyson型集三个形变版本的拟对称极小性,其中一个结果是：设Z是R^d-1中的任一Borel集,h：Z→R¹是Borel函数,满足dim_H（{h≠0}∩Z）=dim_H Z,则h的图G（h）是拟对称极小集,其中h的图G（h）定义为G（h）={（z,y）：z∈Z,y∈[0,h（z）]}.