| D_lambda-n-攀援集的一点注记 |
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| 引用本文： | 符和满, 谭枫. D_lambda-n-攀援集的一点注记[J]. 华南师范大学学报（自然科学版）, 2014, 46(2). |
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| 作者姓名： | 符和满 谭枫 |
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| 作者单位： | 1.1.肇庆学院 |
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| 基金项目： | 国家自然科学基金;国家自然科学青年基金;广东高校优秀青年创新人才培养计划项目 |
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| 摘 要： | 从全空间的角度来研究 $mathcal{D}_lambda$-攀援集. 借助 Furstenberg 族为工具, 把分布攀援集的定义推广到 $mathcal{D}_lambda$-$n$-攀援集, 把关于全空间的分布攀援集的已有结论推广成$mathcal{D}_lambda$-$n$-攀援集的情形. 对任意实数 $lambdain[0,1]$ 和任意整数 $ngeqslant2$, 证得不存在紧致的动力系统以全空间为 $mathcal{D}_lambda$-$n$-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 $mathcal{D}_lambda$-$n$-攀援集.
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| 关 键 词： | 全空间 |
| 收稿时间： | 2013-07-03 |
| 修稿时间： | 2013-09-28 |
A Note on D_lambda-n-Scrambled Sets |
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| A Note on D_lambda-n-Scrambled Sets[J]. Journal of South China Normal University (Natural Science Edition), 2014, 46(2). |
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| Abstract: | The $mathcal{D}_lambda$-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 $mathcal{D}_lambda$-$n$-scrambled set. Then the results on distributionally scrambled sets with the whole space obtained are generalized to the case of $mathcal{D}_lambda$-$n$-scrambled sets. For each real $lambdain[0,1]$ and each integer $ngeqslant2$, the main conclusions are as follows: (1) there is no compact dynamical system with the whole space being a $mathcal{D}_lambda$-$n$-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 $mathcal{D}_lambda$-$n$-scrambled set can be the whole space. |
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| Keywords: | whole space |
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