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拓扑半共轭下扩充与因子Devaney混沌性状的保持性
The Properties of Keeping Each Other on Devaney Chaos between Expansion and Factor under Topologically Semi-conjugate Conditions
【摘要】 讨论了扩充与因子Devaney混沌性状的相互保持,得出在拓扑半共轭条件下,若扩充是Devaney混沌的,则因子也是Devaney混沌的.证明了在有限层覆盖映射与局部等距覆盖映射下,扩充与因子的初值敏感依赖性相互保持.并举例说明即使在局部等距覆盖映射下,由因子的Devaney混沌性推不出扩充的Devaney混沌性.
【Abstract】 In this paper,we discuss Devaney chaos properties of keeping each other between expansion and factor,which educes that if expansion is Devaney chaos,factor is also Devaney chaos on the basis of topologically semi-conjugate.we prove that the property of sensitive dependence on initial condition between expansion and factor is kept each other under finite layer covering map or locally isometric covering map conditions.Through an example,we confirm that even factor is Devaney chaos,we can’t elicit that expansion is Devaney chaos on the base of locally isometric covering map.
【Key words】 topologically semi-conjugate; Devaney chaos; periodically dense; sensitive dependence on initial condition; topologically transitive;
- 【文献出处】 广西师范学院学报(自然科学版) ,Journal of Guangxi Teachers Education University(Natural Science Edition) , 编辑部邮箱 ,2011年04期
- 【分类号】O189.1
- 【下载频次】31