一类低维环面线性映射的周期点及符号分析

上海大学学报(自然科学版)

一类低维环面线性映射的周期点及符号分析

陈浩君1，陈芳跃1,傅新楚2

1.浙江师范大学数学系，浙江金华 321004；
2.上海大学理学院，上海 200444

收稿日期:2006-10-26 修回日期:1900-01-01 出版日期:2008-02-28 发布日期:2008-02-28
通讯作者: 傅新楚

Periodic Points and Symbolic Analysis for Some Low-Dimensional -Linear Torus Maps

CHEN Hao-jun1,CHEN Fang-yue1,FU Xin-chu2

1. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China;
2. College of Sciences, Shanghai University, Shanghai 200444, China

Received:2006-10-26 Revised:1900-01-01 Online:2008-02-28 Published:2008-02-28
Contact: FU Xin-chu2

摘要/Abstract

摘要： 运用符号动力学方法讨论了一类二维环面上分片连续映射的周期点和一族三维环面上分片线性映射的动力学性质.对于这类不连续映射，传统的方法往往失效.通过运用划分及其蕴涵着的编码，给出了其动力学的符号表示及轨道所对应的路径的允字条件.

关键词: 符号表示, 符号动力系统, 允字条件, 周期点

Abstract: In this paper, periodic points of a class of maps on the 2-torus and the dynamics of a class of linear maps on the 3-torus are discussed. Using codes underlying the map operations, symbolic descriptions of the dynamics and admissibility conditions for itineraries are given for these discontinuous maps.

Key words: admissibility condition, symbolic description, symbolic dynamical system, periodic point

中图分类号:

O175.12

陈浩君;陈芳跃;傅新楚. 一类低维环面线性映射的周期点及符号分析[J]. 上海大学学报(自然科学版).

CHEN Hao-jun;CHEN Fang-yue;FU Xin-chu. Periodic Points and Symbolic Analysis for Some Low-Dimensional -Linear Torus Maps[J]. Journal of Shanghai University（Natural Science Edition）.