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Single-Valley-Extended Solutions with Platforms of FKS Equation

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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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  1. Numerical Simulation Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang, 641100, Sichuan, People’s Republic of China

    Yong-Guo Shi

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  1. Yong-Guo Shi
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Correspondence to Yong-Guo Shi.

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A Project Supported by Scientific Research Fund of SiChuan Provincial Education Department (18ZA0274).

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Shi, YG. Single-Valley-Extended Solutions with Platforms of FKS Equation. Results Math 75, 178 (2020). https://doi.org/10.1007/s00025-020-01307-z

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  • DOI: https://doi.org/10.1007/s00025-020-01307-z

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