Existence Domain Analysis and Numerical Algorithm of Fixed Point for Generalized 3x+1 Function T(x)

LIU Shuai; CHE Xiang-jiu; WANG Zheng-xuan

您当前的位置：

首页 >

文章列表页 >

Existence Domain Analysis and Numerical Algorithm of Fixed Point for Generalized 3x+1 Function T(x)

更新时间：2025-07-16

- Existence Domain Analysis and Numerical Algorithm of Fixed Point for Generalized 3x+1 Function T(x)
- Acta Electronica Sinica Vol. 39, Issue 10, Pages: 2282-2287(2011)
- 作者机构：
  
  吉林大学计算机科学与技术学院,吉林,长春,130021
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP301
- Published：2011
- 稿件说明：
移动端阅览
LIU Shuai, CHE Xiang-jiu, WANG Zheng-xuan. Existence Domain Analysis and Numerical Algorithm of Fixed Point for Generalized 3x+1 Function T(x)[J]. Acta Electronica Sinica, 2011, 39(10): 2282-2287.
DOI：

LIU Shuai, CHE Xiang-jiu, WANG Zheng-xuan. Existence Domain Analysis and Numerical Algorithm of Fixed Point for Generalized 3x+1 Function T(x)[J]. Acta Electronica Sinica, 2011, 39(10): 2282-2287. DOI：

摘要

+1推广函数

(

)的不动点性质及存在区域分析是分形中的一个重要研究问题.

(

)是结构复杂的超越函数

其在复平面上的不动点难于求解

不动点性质难于估计

这成为进一步研究

(

)动力系统的一个障碍.首先通过

(

)的拓扑不变性

给出了

(

)在复平面上存在不动点的构造性证明

分析了不动点的存在区域及其性质.根据存在区域

给出了

(

)的不动点在复平面上的分布.通过不动点的分布

提出了一种求

(

)不动点的数值算法.找到了

(

)在复平面上的多个收敛域

并绘制了收敛域处的分形图形.数值实验结果表明

本文算法正确、简捷.

Abstract

For generalized 3

+1 function

(

)

the feature of fixed points and their existence-domain analysis is an important problem in fractal.

(

) is a complex transcendental function and its fixed point in C-plane is hardly to solve.Meanwhile

the feature of fixed point is difficult to analyze.All these become an obstacle for the further study of

(

) dynamic system.In this paper

Because of the topological invariance of

(

)

we constructively proved its fixed point in C-plane firstly.Then we give the analysis for the existence domain of fixed points as well as their feature.Based on the existence do

main of

(

) fixed points

we estimated their distributions in C-plane.So we put forward a numerical algorithm for solving the fixed points of

(

) by analyzed the basis of distributions.Furthermore

we obtained some convergence domains of

(

) in C-plane and drew fractal image of these domains.The result of numerical experiment shows that the algorithm in this paper is correct and easy to implement.

关键词

Keywords

references

Views

1082

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

A Miniaturized Broadband Planar Lens Antenna with High Transmittance Based on Fractal Metasurface

Back Scattering RCS of Two-Dimensional Sea Fractal Surface

Channel Estimation Based on Fractal Filter for cdma2000

Pressure Drop and Heat Transfer in Fractal Microchannel Heat Sinks for Cooling of Electronic Chips

Related Author

MA Li-na

GU Chang-zhan

ZHOU Ling-yun

MAO Jun-fa

YUAN Da

FAN Hui

ZHANG Cai-ming

LI Jin-jiang

Related Institution

MoE Key Laboratory of High-Speed Electronic Systems， Shanghai Jiao Tong University

MoE Key Laboratory of Artificial Intelligence， Shanghai Jiao Tong University

Key Laboratory of Electromagnetic Spatial Information， Chinese Academy of Sciences

School of Computer Science and TechnologyShandong Institute of Economic and TechnologyYantaiShandong 264005China

School of Computer Science and Technology, Shandong University

⁰