Single-valley solutions of the second type of FKS equation
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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.
KeywordsFeigenbaum–Kadanoff–Shenker equation The second type of FKS equation All single-valley solutions Single-peak even solutions
Mathematics Subject Classification39B12 39B22
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