| Fengenbaum映射的搓揉序列与特征集 |
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| 引用本文： | 廖公夫,王立冬,杨柳.Fengenbaum映射的搓揉序列与特征集[J].数学学报,2006,49(2):399-404. |
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| 作者姓名： | 廖公夫 王立冬 杨柳 |
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| 作者单位： | [1]吉林大学数学学院,长春130012 [2]大连民族学院应用数学系,大连116600 |
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| 基金项目： | 国家自然科学基金资助项目（19971035）;吉林大学创新基金资助项目（2004C8051） |
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| 摘 要： | 设f为Feigenbaum映射,亦即函数方程fp(λx)=λf(x)满足一定条件的单峰解．f的搓揉序列为0-1无限序列,f的特征集是临界点轨迹的闭包．本文研究f的性质进而证明．f的搓揉序列是某代换在符号空间中的不动点,f在特征集上的限制是某代换子移位的一个因子．
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| 关 键 词： | Fengenbaum映射 搓揉序列 代换系统 |
| 文章编号： | 0583-1431（2006）02-0399-06 |
| 收稿时间： | 2004-09-06 |
| 修稿时间： | 2004-09-062005-02-18 |
Kneading Sequences and Characteristic Sets of Feigenbaum's Maps |
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| Gong Fu LI, AOLi Dong WANG, Liu YANG.Kneading Sequences and Characteristic Sets of Feigenbaum''s Maps[J].Acta Mathematica Sinica,2006,49(2):399-404. |
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| Authors: | Gong Fu LI AOLi Dong WANG Liu YANG |
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| Institution: | Institute of Mathematics, Jilin University, Changchun 130012, P. R. China; Department of Applied Mathematics, Dalian Nationals University, Dalian 116600, P. R. China; Institute of Mathematics, Jilin University, Changehun 130012, P. R. China |
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| Abstract: | Let f be a Feigenbaum map, i.e. a unimodal solution satisfying certain conditions of the functional equation fp(λx) =λf(x) . The kneading sequence of f is a 0-1 infinite sequence and the characteristic set of f is the closure of the orbit of critical point. In this paper, we investigate properties of f and then we prove that the kneading sequence of f is a fixed point of some substitution in a symbolic space and the restriction of f to characteristic set is a factor of some substitution subshift. |
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| Keywords: | Feigenbaum map kneading sequence substitution system |
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