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)

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Abstrakt

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.

Język oryginału	angielski
Strony (od–do)	3005-3016
Liczba stron	12
Czasopismo	International Journal of Bifurcation and Chaos
Tom	19
Numer wydania	9
Identyfikatory DOI	https://doi.org/10.1142/S021812740902461X
Status publikacji	Opublikowano - wrz 2009

Obszary tematyczne ASJC Scopus

Modelowanie i symulacja
Inżynieria (różne)
Multidyscyplinarne
Matematyka stosowana

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10.1142/S021812740902461X

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

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.",

keywords = "Carmichael function, Chaos, Chebyshev polynomials, Fixed points, Minimal polynomials, Periodic points",

author = "Roman Witua and Damian S{\l}ota",

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AU - Witua, Roman

AU - Słota, Damian

PY - 2009/9

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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

U2 - 10.1142/S021812740902461X

DO - 10.1142/S021812740902461X

M3 - Article

AN - SCOPUS:73149103728

SN - 0218-1274

VL - 19

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)

Abstrakt

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