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On the Three, Five and Other Periodic Orbits of Some Polynomials

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Book cover Analysis and Simulation of Electrical and Computer Systems

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 324))

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Abstract

In the paper all three and five periodic orbits of certain (known and a bit less known) quadratic and cubic polynomials as well as polynomials of order greater than 4 are generated. Other periodic orbits are also discussed here. The basic polynomials considered in this paper are the minimal polynomials of \(2\mathop {\cos } \frac{2\pi }{2n - 1}\) or \(2\mathop {\sin } \frac{2\pi }{2n - 1}\) for every \(n = 4,5,6,7,8\). The concept of n-periodic trigonometric orbits is introduced. Also generalizations of Benedetto identities are presented.

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Authors and Affiliations

  1. Institute of Mathematics, Silesian University of Technology, Gliwice, Poland

    Roman Wituła, Edyta Hetmaniok & Damian Słota

  2. Department of Mechatronics, Faculty of Electrical Engineering, Silesian University of Technology, Gliwice, Poland

    Tomasz Trawiński & Wojciech Kołton

Authors
  1. Roman Wituła
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  2. Edyta Hetmaniok
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  3. Damian Słota
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  4. Tomasz Trawiński
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  5. Wojciech Kołton
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Corresponding author

Correspondence to Roman Wituła .

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Editors and Affiliations

  1. Department of Electrical and Computer Engineering Fundamentals, Rzeszów University of Technology, Rzeszów, Poland

    Lesław Gołębiowski

  2. Department of Electrical and Computer Engineering Fundamentals, Rzeszów University of Technology, Rzeszów, Poland

    Damian Mazur

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Wituła, R., Hetmaniok, E., Słota, D., Trawiński, T., Kołton, W. (2015). On the Three, Five and Other Periodic Orbits of Some Polynomials. In: Gołębiowski, L., Mazur, D. (eds) Analysis and Simulation of Electrical and Computer Systems. Lecture Notes in Electrical Engineering, vol 324. Springer, Cham. https://doi.org/10.1007/978-3-319-11248-0_8

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  • DOI: https://doi.org/10.1007/978-3-319-11248-0_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11247-3

  • Online ISBN: 978-3-319-11248-0

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