3阶非单谷Feigenbaum映射的拟极限集

一个从闭区间到自身的连续映射被称为3阶非单谷Feigenbaum映射,如果它是函数方程f~3(λx)=λf(x)的解．本文讨论了3阶非单谷Feigenbaum映射的拟极限集及其Hausdorff维数．3阶非单谷Feigenbaum映射必然产生混沌,混沌的产生使得拟极限集的存在性问题复杂化．文中采用分形几何中的知识方法证明了此类映射的拟极限集的存在性,并相应的对其Hausdorff维数作出了估计．最后给了一个具体的例子,说明确实存在这样的3阶非单谷Feigenbaum映射．

Likely Limit Sets of 3-Order Nonsingle-Valley Feigenbaum's Maps

A continuous map from a closed interval into itself is a 3-order Feigenbaum's map if it is a solution of the functional equation f~3(λx)=λf(x).We consider the likely limit sets of 3-order nonsingle-valley Feigenbaum's maps and their Hausdorff dimensions.3-order nonsingle-valley Feigenbaum's maps must bring about chaos,and chaos also brings about the complication of the problem on the existence of likely limit sets.We testify the existence of the maps' likely limit sets by using the method of fractal geometry,estimate their Hausdorff dimensions.As an application,we give a idiographic example in order to prove the existence of 3-order nonsingle-valley Feigenbaum's maps.