不具有简单轨的4阶非单谷Feigenbaum映射的拟极限集  

Likely limit sets of 4-order nonsingle-valley Feigenbaum's maps without simple periodic orbits

作　　者：王立娟[1] 张爱华[1] 

机构地区：[1]吉林大学数学学院数学系,长春130012

出　　处：《吉林大学学报（理学版）》2004年第4期499-502,共4页Journal of Jilin University:Science Edition

摘　　要：讨论一类不具有简单轨的4阶Feigenbaum映射拟极限集的存在条件及其Hausdorff维数.不具有简单轨的4阶Feigenbaum映射必然产生混沌,从而使拟极限集的存在性问题复杂化.利用分形几何中的方法证明了此类映射拟极限集的存在性,并相应的对其Hausdorff维数做出估计.最后给一个具体例子,说明确实存在不具有简单轨的4阶Feigenbaum映射.4-order nonsingle-valley Feigenbaum's maps without simple periodic orbits must bring chaos, chaos also bring the complication of the problem on the existence of likely limit sets. We testified the existence of the maps' likely limit sets using the method of fractal geometry and estimated their Hausdorff dimension. In the end, we gave an idiographic example to proof the existence of 4-order nonsingle-valley Feigenbaum's maps without simple periodic orbits.

关 键 词：FEIGENBAUM映射 极限集 HAUSDORFF维数 证明 存在条件 分形几何 估计 例子 混沌 

分 类 号：O189[理学—数学] O175[理学—基础数学]