共查询到20条相似文献,搜索用时 203 毫秒
1.
尹永成 《数学年刊A辑(中文版)》1999,(5)
本文证明了半双曲有理映射Julia集的局部连通性,推广了Carleson-Jones-Yoccoz关于多项式的结果,同时还考虑了半双曲有理映射Julia集的面积问题. 相似文献
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线段上的连续自映射,当周期点集为闭集时,其轨道十分简单,当然,动力系统不会是混乱的,因此,研究周期点集的聚点的极限性态与混乱的关系,无疑可以进一步揭示混乱现象产生的原因。文[6]证明了当回归点集非闭,f是混乱的。本文则给出了周期点集非闭时f为混乱的充分条件。这说明了只要周期点集非闭动力系统就可能是混乱的。 相似文献
4.
主要讨论区间映射的链回归点的可链点集与链等价集的关系,证明了:若区间映射的拓扑熵是零,则它的链回归点的可链点集与链等价集相等.此外还得到了区间映射有正拓扑熵的几个等价条件. 相似文献
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考虑金刚石型等级晶格上的Potts模型, 研究了复相位对应点集的性质. 这些集合事实上是一族有理映射的Fatou集. 就其拓扑结构给出了比较完备的刻画. 相似文献
7.
集值映射最优化的问题的严有效解集的连通性及应用 总被引:4,自引:0,他引:4
仇秋生 《高校应用数学学报(A辑)》1999,(1):85-92
本文对集值映射最优化问题引入严有效解的概念,证明了当目标函数为锥类凸的集值映射时,其目标空间的严有效点集是连通的; 相似文献
8.
连续树映射非游荡集的拓扑结构 总被引:10,自引:0,他引:10
顾荣宝 《数学年刊A辑(中文版)》1998,(5)
本文研究树(即不含有圈的一维紧致连通的分支流形)上连续自映射的非游荡集的拓扑结构.证明了孤立的周期点都是孤立的非游荡点;具有无限轨道的非游荡点集的聚点都是周期点集的二阶聚点,以及ω-极限集的导集等于周期点集的导集和非游荡集的二阶导集等于周期点集的二阶导集. 相似文献
9.
张增喜 《数学的实践与认识》2004,34(9):127-129
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 . 相似文献
10.
集值映射最优化问题的严有效解集的连通性及应用 总被引:7,自引:0,他引:7
仇秋生 《高校应用数学学报(A辑)》1999,14(1):11
本文对集值映射最优化问题引入严有效解的概念.证明了当目标函数为锥类凸的集值映射时,其目标空间里的严有效点集是连通的;若目标函数为锥凸的集值映射时,其严有效解集也是连通的.作为应用,讨论了超有效解集的连通性. 相似文献
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We obtain residue formulae for certain functions of several variables. As an application, we obtain closed formulae for vector partition functions and for their continuous analogs. They imply an Euler-MacLaurin summation formula for vector partition functions, and for rational convex polytopes as well: we express the sum of values of a polynomial function at all lattice points of a rational convex polytope in terms of the variation of the integral of the function over the deformed polytope.
14.
孙道椿 《数学物理学报(A辑)》2006,26(2):161-167
该文运用Hausdorff意义下的极限研究了有理动力系统的Julia集, 用新的思路证明了几个关于Julia集的定理. 为计算机作Julia集提供了更多的理论根据. 相似文献
15.
QIAO Jianyong Center of Mathematics China University of Mining Technology Beijing China 《中国科学A辑(英文版)》2005,48(4):433-447
The sets of the points corresponding to the complex phases of the Potts model on the diamond hierarchcal lattice are studied. These sets are the Fatou sets of a family of rational mappings. The topological structures of these sets are described completely. 相似文献
16.
The theory of heights for rational points on arithmetic ellipticcurves is becoming well known. An important fact in the basictheory is the relationship between the naïve and the canonicalheight of a rational point; in fact, they differ by a uniformlybounded amount. The paper provides a generalisation of thisfact from the point of view of heights of polynomials, ratherthan heights of points. This concept is extended to polynomialsin several variables. 相似文献
17.
Chunhua Hu Shaoyong Lai Zheng Dou 《Journal of Difference Equations and Applications》2019,25(3):351-372
A rational expectation model with lagged endogenous variables is used to describe how the current price level is influenced by the expectation and historic price level. The time domain of the rational expectation model is extended to a complex discrete time domain which is a collection of points along the real number line. The rational expectation model with lagged endogenous variables is solved in multi-dimensional cases where the agents possess multiple assets, and the current price of each asset is related to the expected price and historical prices. An example about price determination process of storable commodities is given to illustrate the advantages of the rational expectation model on isolate time domain. 相似文献
18.
《复变函数与椭圆型方程》2012,57(12):991-1003
The criterion for linearizability is obtained by a property of denominator of rational numbers that are given by continued fractions. We can regard this criterion as a condition given by behaviors of orbits of dynamical systems of translation groups on a one-dimensional real torus. By using continued fractions, we obtain a criterion that is an analogous phenomenon in several complex variables that is determined by behaviors of dynamical systems of translation groups on a one-dimensional complex torus. 相似文献
19.
《Chaos, solitons, and fractals》2002,13(2):233-243
Schröder iteration functions, a generalization of the Newton–Raphson method to determine roots of equations, are generally rational functions which possess some critical points, free to converge to attracting cycles. These free critical points, however, satisfy some higher-degree polynomial equations which we solve analytically. Then, with the help of microcomputer plots, we examine the Julia sets of the Schröder functions and the orbits of all their free critical points associated with a particular one-parameter family of quartic polynomials, by walking in their dynamic and parameter spaces. This examination takes place in the complex plane as well as on the Riemann sphere. 相似文献
20.
A. B. Shidlovskii 《Mathematical Notes》2000,68(5-6):644-651
The paper presents several theorems on the linear and algebraic independence of the values at algebraic points of the set of E-functions related by algebraic equations over the field of rational functions, as well as some estimates of the absolute values of polynomials with integer coefficients in the values of such functions. The results are obtained by using the properties of ideals in the ring of polynomials of several variables formed by equations relating the above functions over the field of rational functions. 相似文献