Fixed and periodic points of polynomials generated by minimal polynomials of 2cos(2π/n)

Roman Witua; Damian Słota

doi:10.1142/S021812740902461X

Fixed and periodic points of polynomials generated by minimal polynomials of 2cos(2π/n)

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this paper certain identities are generated for minimal polynomials Θ_n(z) of numbers 2cos(2π/n) and for Chebyshev polynomials of the first kind. Against the background of these identities, sets of cyclic points of some modified versions of these polynomials are derived. The discussion leads to the analysis of a certain new counting sequence of numbers connected with Carmichael function.

Original language	English
Pages (from-to)	3005-3016
Number of pages	12
Journal	International Journal of Bifurcation and Chaos
Volume	19
Issue number	9
DOIs	https://doi.org/10.1142/S021812740902461X
Publication status	Published - Sept 2009

Keywords

Carmichael function
Chaos
Chebyshev polynomials
Fixed points
Minimal polynomials
Periodic points

ASJC Scopus subject areas

Modeling and Simulation
Engineering (miscellaneous)
Multidisciplinary
Applied Mathematics

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10.1142/S021812740902461X

Cite this

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abstract = "In this paper certain identities are generated for minimal polynomials Θn(z) of numbers 2cos(2π/n) and for Chebyshev polynomials of the first kind. Against the background of these identities, sets of cyclic points of some modified versions of these polynomials are derived. The discussion leads to the analysis of a certain new counting sequence of numbers connected with Carmichael function.",

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AU - Słota, Damian

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N2 - In this paper certain identities are generated for minimal polynomials Θn(z) of numbers 2cos(2π/n) and for Chebyshev polynomials of the first kind. Against the background of these identities, sets of cyclic points of some modified versions of these polynomials are derived. The discussion leads to the analysis of a certain new counting sequence of numbers connected with Carmichael function.

AB - In this paper certain identities are generated for minimal polynomials Θn(z) of numbers 2cos(2π/n) and for Chebyshev polynomials of the first kind. Against the background of these identities, sets of cyclic points of some modified versions of these polynomials are derived. The discussion leads to the analysis of a certain new counting sequence of numbers connected with Carmichael function.

KW - Carmichael function

KW - Chaos

KW - Chebyshev polynomials

KW - Fixed points

KW - Minimal polynomials

KW - Periodic points

UR - https://www.scopus.com/pages/publications/73149103728

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DO - 10.1142/S021812740902461X

M3 - Article

AN - SCOPUS:73149103728

SN - 0218-1274

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SP - 3005

EP - 3016

JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

IS - 9

ER -

Fixed and periodic points of polynomials generated by minimal polynomials of 2cos(2π/n)

Abstract

Keywords

ASJC Scopus subject areas

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