摘要
从全空间的角度来研究Dλ-攀援集.借助Furstenberg族为工具,把分布攀援集的定义推广到Dλ-n-攀援集,把关于全空间的分布攀援集的已有结论推广成Dλ-n-攀援集的情形.对任意实数λ∈[0,1]和任意整数n≥2,证得不存在紧致的动力系统以全空间为Dλ-n-攀援集;并且构造出了只含可数多个点的非紧致的可逆系统,以全空间为Dλ-n-攀援集.
The Dλ-scrambled sets are to be analysed in the aspect of whole space. By means of Furstenberg families, the definition of distributionally scrambled set is extended to define a Dλ-n-scrambled set. Then the results on distributionally scrambled sets with the whole space obtained are generalized to the case of Dλ-n-scrambled sets. For each real λ∈[0,1] and each integer n≥2, the main conclusions are as follows: (1) there is no compact dynamical system with the whole space being a Dλ-n-scrambled set; (2) based on the example provided by WANG et al, an invertible noncompact dynamical system consisting of countable many points are constructed, whose Dλ-n-scrambled set can be the whole space.
出处
《华南师范大学学报(自然科学版)》
CAS
北大核心
2014年第2期34-37,共4页
Journal of South China Normal University(Natural Science Edition)
基金
国家自然科学基金项目(11071084
11201157)
广东高校优秀青年创新人才培养计划项目(2012LYM_0133)