Iterative roots of piecewise monotonic functions with finite nonmonotonicity height

作者：Li Lin; Chen Jingmin^*

来源：Journal of Mathematical Analysis and Applications, 2014, 411(1): 395-404.

DOI：10.1016/j.jmaa.2013.09.051

• Iterative root
• Piecewise monotonic function
• Nonmonotonicity height
• Fort
• Interval sequence

It is known that any continuous piecewise monotonic function with nonmonotonicity height not less than 2 has no continuous iterative roots of order n greater than the number of forts of the function. In this paper, we consider the problem of iterative roots in the case that the order n is less than or equal to the number of forts. By investigating the trajectory of possible continuous roots, we give a general method to find all iterative roots of those functions with finite nonmonotonicity height.

• 出版日期2014-3-1
• 单位嘉兴学院; 四川大学