Single-valley-extended solutions with platforms of FKS equation
Yong-Guo Shi
TL;DR
This paper introduces a new type of FKS equation and constructs continuous solutions with platforms, expanding understanding of quasiperiodic routes to chaos in circle maps.
Contribution
It proposes a second type of FKS equation and develops a novel iterative method to find continuous solutions with platforms for this equation.
Findings
New second type of FKS equation introduced
Constructed continuous solutions with platforms
Established relationships between solutions of the two FKS equations
Abstract
The Feigenbaum-Kadanoff-Shenker (FKS) equation is a nonlinear iterative functional equation, which characterizes the quasiperiodic route to chaos for circle maps. Instead of FKS equation, we put forward the second type of FKS equation. We use the iterative construction method to obtain a new kind of continuous solutions with platforms for this functional equation. We show some properties of these continuous solutions, and give one relationship of some solutions between FKS equation and the second type of FKS equation.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Advanced Differential Equations and Dynamical Systems · Mathematical Dynamics and Fractals