Computational Experiments with the Roots of Fibonacci-like Polynomials as a Window to Mathematics Research

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Computational Experiments with the Roots of Fibonacci-like Polynomials as a Window to Mathematics Research. / Abramovich, Sergei; Kuznetsov, Nikolay V.; Leonov, Gennady A.

In: Axioms, Vol. 11, No. 2, 48, 02.2022.

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

BibTeX

@article{c28862e7f60f46c792a549256203fbf7,

title = "Computational Experiments with the Roots of Fibonacci-like Polynomials as a Window to Mathematics Research",

abstract = "Fibonacci-like polynomials, the roots of which are responsible for a cyclic behavior of orbits of a second-order two-parametric difference equation, are considered. Using Maple andWolfram Alpha, the location of the largest and the smallest roots responsible for the cycles of period p among the roots responsible for the cycles of periods 2kp (period-doubling) and kp (period-multiplying) has been determined. These purely computational results of experimental mathematics, made possible by the use of modern digital tools, can be used as a motivation for confirmation through not-yet-developed methods of formal mathematics.",

keywords = "Computational experiments, Cycles, Fibonacci-like polynomials, Generalized golden ratios, Maple, Wolfram Alpha",

author = "Sergei Abramovich and Kuznetsov, {Nikolay V.} and Leonov, {Gennady A.}",

note = "Publisher Copyright: {\textcopyright} 2022 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2022",

month = feb,

doi = "10.3390/axioms11020048",

language = "English",

volume = "11",

journal = "Axioms",

issn = "2075-1680",

publisher = "MDPI AG",

number = "2",

}

RIS

TY - JOUR

T1 - Computational Experiments with the Roots of Fibonacci-like Polynomials as a Window to Mathematics Research

AU - Abramovich, Sergei

AU - Kuznetsov, Nikolay V.

AU - Leonov, Gennady A.

PY - 2022/2

Y1 - 2022/2

N2 - Fibonacci-like polynomials, the roots of which are responsible for a cyclic behavior of orbits of a second-order two-parametric difference equation, are considered. Using Maple andWolfram Alpha, the location of the largest and the smallest roots responsible for the cycles of period p among the roots responsible for the cycles of periods 2kp (period-doubling) and kp (period-multiplying) has been determined. These purely computational results of experimental mathematics, made possible by the use of modern digital tools, can be used as a motivation for confirmation through not-yet-developed methods of formal mathematics.

AB - Fibonacci-like polynomials, the roots of which are responsible for a cyclic behavior of orbits of a second-order two-parametric difference equation, are considered. Using Maple andWolfram Alpha, the location of the largest and the smallest roots responsible for the cycles of period p among the roots responsible for the cycles of periods 2kp (period-doubling) and kp (period-multiplying) has been determined. These purely computational results of experimental mathematics, made possible by the use of modern digital tools, can be used as a motivation for confirmation through not-yet-developed methods of formal mathematics.

KW - Computational experiments

KW - Cycles

KW - Fibonacci-like polynomials

KW - Generalized golden ratios

KW - Maple

KW - Wolfram Alpha

UR - http://www.scopus.com/inward/record.url?scp=85123897422&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/ff867ad6-de65-3aba-8d1e-8256375119ae/

U2 - 10.3390/axioms11020048

DO - 10.3390/axioms11020048

M3 - Article

AN - SCOPUS:85123897422

VL - 11

JO - Axioms

JF - Axioms

SN - 2075-1680

IS - 2

M1 - 48

ER -

ID: 95230641