Skip to main content
SpringerLink
Log in

Multi-Modal-Extended Solutions of FKS Equation

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

The Feigenbaum–Kadanoff–Shenker (FKS) equation characterizes the quasiperiodic route to chaos for circle maps. We consider the second type of FKS equation, which is also a nonlinear iterative functional equation. Some properties of continuous solutions are summarized. Using the iterative construction method, we obtain some multi-modal-extended solutions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Briggs, K.M., Dixon, T.W., Szekeres, G.: Analytic solutions of the Cvitanović–Feigenbaum and Feigenbaum–Kadanoff–Shenker equations. Int. J. Bifurcat. Chaos 8, 347–357 (1998)

    Article  Google Scholar 

  2. Feigenbaum, M.J., Kadanoff, L.P., Shenker, S.J.: Quasiperiodicity in dissipative systems: a renormalization group analysis. Phys. D 5, 370–386 (1982)

    Article  MathSciNet  Google Scholar 

  3. Kuczma, M.: Functional Equations in a Single Variable. Polish Scientific Publishers, Warszawa (1968)

    MATH  Google Scholar 

  4. Shi, Y.G.: Single-valley solutions of the second type of FKS equation. Aequationes Math. 93, 919–925 (2019)

    Article  MathSciNet  Google Scholar 

  5. Shi, Y.G.: Differentiable solutions of the Feigenbaum–Kadanoff–Shenker equation. Discrete Contin. Dyn. Syst. B. 25, 4575–4583 (2020)

    MathSciNet  MATH  Google Scholar 

  6. Shi, Y.G.: Single-valley-extended solutions with platforms of FKS equation. Results Math 75, 178 (2020)

    Article  MathSciNet  Google Scholar 

Download references

Funding

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

Author information

Authors and Affiliations

  1. College of Mathematics and Information Science, Neijiang Normal University, Neijiang, 641100, Sichuan, People’s Republic of China

    Yong-Guo Shi

Authors
  1. Yong-Guo Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yong-Guo Shi.

Ethics declarations

Conflict of interest

No conflict of interest exits in the submission of this manuscript. The work was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All the authors listed have approved the manuscript..

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shi, YG. Multi-Modal-Extended Solutions of FKS Equation. Results Math 76, 213 (2021). https://doi.org/10.1007/s00025-021-01528-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00025-021-01528-w

Keywords

Mathematics Subject Classification

Search

Navigation