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Finding Orbits of Functions Using Suffridge Polynomials

  • Dmitriy Dmitrishin
  • Paul HagelsteinEmail author
  • Alex Stokolos
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

In this paper we indicate how Suffridge polynomials may be used to find orbits of functions. In particular, we describe a control mechanism that, given a function \(f: \mathbb {R}^n \rightarrow \mathbb {R}^n\) and a positive integer T, yields a dynamical system \(G: \mathbb {R}^{Tn} \rightarrow \mathbb {R}^{Tn}\) that under quantifiable conditions has (x, …, x) as an attractor provided x lies on a T-cycle of f. An explicit example of this control mechanism is provided using a logistic function.

Keywords

Control theory Stability 

2010 Mathematics Subject Classification

Primary 93B52 42A05 

Notes

Acknowledgements

We wish to thank the referee for a careful reading of the paper.

P. H. is partially supported by a grant from the Simons Foundation (#521719 to Paul Hagelstein).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Dmitriy Dmitrishin
    • 1
  • Paul Hagelstein
    • 2
    Email author
  • Alex Stokolos
    • 3
  1. 1.Odessa National Polytechnic UniversityOdessaUkraine
  2. 2.Department of MathematicsBaylor UniversityWacoUSA
  3. 3.Department of Mathematical SciencesGeorgia Southern UniversityStatesboroUSA

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