变参数动力系统的扩张性

通常情况下,人们所关心的经典动力系统是由某个唯一映射迭代所产生的,随着混沌理论的的发展,映射迭代的唯一性在2006年被田传俊和陈关荣发表的一篇关于度量空间中一列连续自映射序列混沌性的文章打破,该文章提出变参数动力系统的概念,给出了周期点、混合性、回复性、传递性、扩张性等概念,但没有进行详细的深讨。笔者在此基础上来研究变参数动力系统的扩张性并提出了s次齐次迭代系统的思想,从而进一步拓展了离散动力系统的研究范围。主要将扩张性在固定参数动力系统中的拓扑共轭不变性推广到变参数动力系统中,给出了s次齐次迭代的概念和扩张性蕴含有限个不动点的结论,并说明了扩张性与生成子的存在性等价。

Expansion of variable-parameter dynamical system

Usually,the classical dynamical systems people concerned are generated by a unique mapping in iterative way,and as the development of chaos theory,the uniqueness of iterative mapping is broken by professor Tian Chuanjun and Chen Guanrong,and they put forward the concept of variable parameter dynamical systems in a paper on chaos of a sequence of maps in metric space in 2006.Although some concepts such as periodic point,mixed,recurrence,transitivity,expansion in the paper are given,but are not discussed in detail.We study on expansion of variable parameters dynamical system and puts forward the idea of s-order homogeneous iterative systems in order to expand the scope of the study of discrete dynamical system.This paper mainly shows the expansion that is topological conjugate invariants in fixed-parameter dynamical system can be extended to variable-parameter dynamical system,gives a new concept of s-order homogeneous iterative,got the conclusion that if a variable-parameter dynamical system is expansionary then it only has finite fixed points,and explaines that expansion is equivalent to existence of generators.