Complexity in iteration of polynomials

  • Zhiheng Yu
  • Liu LiuEmail author


In order to discuss the complexity of nonmonotonicity of a given PM function, it is needed to determine the height of PM functions. But it is not easy to do even for a polynomial because there are great difficulties in determining the number of real zeros for polynomials of higher degrees. In this paper we introduce two iterative sets to determine the nonmonotonicity height for polynomials and give a numerical algorithm for computing the height of general polynomials.


Polynomials Nonmonotonicity height Level set Descendants 

Mathematics Subject Classification

26A18 39B12 68W30 



The authors are very grateful to Professor Weinian Zhang for his several valuable suggestions and corrections in our expression. The authors also sincerely thank the referees for their encouragement and helpful comments and suggestions.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsSouthwest Jiaotong UniversityChengduPeople’s Republic of China

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