Single-valley solutions of the second type of FKS equation

  • Yong-Guo ShiEmail author


The Feigenbaum–Kadanoff–Shenker (FKS) equation for universal scaling in circle maps characterizes the quasiperiodic route to chaos. We reduce the FKS equation to another type of equation, and prove that they are equivalent to each other in the sense of unimodal solutions. We present some properties of these solutions. According to the range of parameters, we give two algorithms to obtain all unimodal solutions.


Feigenbaum–Kadanoff–Shenker equation The second type of FKS equation All single-valley solutions Single-peak even solutions 

Mathematics Subject Classification

39B12 39B22 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information ScienceNeijiang Normal UniversityNeijiangPeople’s Republic of China

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