Fibonacci-Type Polynomials as a Trajectory of a Discrete Dynamical System

Matthew He; Davis P. Simon; Paolo E. Ricci

Fibonacci-Type Polynomials as a Trajectory of a Discrete Dynamical System

Matthew He
, Davis P. Simon
, Paolo E. Ricci

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

Abstract

Families of polynomials which obey the Fibonacci recursion relation can be generated by repeated iterations of a 2×2 matrix,Q 2, acting on an initial value matrix, R 2. One matrix fixes the recursion relation, while the other one distinguishes between the different polynomial families. Each family of polynomials can be considered as a single trajectory of a discrete dynamical system whose dynamics are determined by Q 2. The starting point for each trajectory is fixed by R 2(x). The forms of these matrices are studied, and some consequences for the properties of the corresponding polynomials are obtained. The main results generalize to the so-called r-Bonacci polynomials. © 2002 Springer.

Original language	American English
Pages (from-to)	367-374
Number of pages	8
Journal	Rendiconti Del Circolo Matematico Di Palermo
Volume	51
Issue number	2
State	Published - Jun 1 2002

Funding

This research has been partially supported by K. C. Wong Education Foundation, Hong Kong, while the first author was visiting the Institute of Computational Mathematics and Scientific/Engineering Computing (ICMSEC) of Chinese Academy of Sciences (CAS) in Beijing. The author is grateful to Professor Ya-xiang Yuan and Dr. Yu-hong Dai of ICMSEC for making such a visit possible.

Funders
Chinese Academy of Sciences
K. C. Wong Education Foundation

ASJC Scopus Subject Areas

General Mathematics

Disciplines

Mathematics

Cite this

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abstract = "Families of polynomials which obey the Fibonacci recursion relation can be generated by repeated iterations of a 2×2 matrix,Q 2, acting on an initial value matrix, R 2. One matrix fixes the recursion relation, while the other one distinguishes between the different polynomial families. Each family of polynomials can be considered as a single trajectory of a discrete dynamical system whose dynamics are determined by Q 2. The starting point for each trajectory is fixed by R 2(x). The forms of these matrices are studied, and some consequences for the properties of the corresponding polynomials are obtained. The main results generalize to the so-called r-Bonacci polynomials. {\textcopyright} 2002 Springer.",

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AU - Simon, Davis P.

AU - Ricci, Paolo E.

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N2 - Families of polynomials which obey the Fibonacci recursion relation can be generated by repeated iterations of a 2×2 matrix,Q 2, acting on an initial value matrix, R 2. One matrix fixes the recursion relation, while the other one distinguishes between the different polynomial families. Each family of polynomials can be considered as a single trajectory of a discrete dynamical system whose dynamics are determined by Q 2. The starting point for each trajectory is fixed by R 2(x). The forms of these matrices are studied, and some consequences for the properties of the corresponding polynomials are obtained. The main results generalize to the so-called r-Bonacci polynomials. © 2002 Springer.

AB - Families of polynomials which obey the Fibonacci recursion relation can be generated by repeated iterations of a 2×2 matrix,Q 2, acting on an initial value matrix, R 2. One matrix fixes the recursion relation, while the other one distinguishes between the different polynomial families. Each family of polynomials can be considered as a single trajectory of a discrete dynamical system whose dynamics are determined by Q 2. The starting point for each trajectory is fixed by R 2(x). The forms of these matrices are studied, and some consequences for the properties of the corresponding polynomials are obtained. The main results generalize to the so-called r-Bonacci polynomials. © 2002 Springer.

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IS - 2

ER -

Fibonacci-Type Polynomials as a Trajectory of a Discrete Dynamical System

Abstract

Funding

ASJC Scopus Subject Areas

Disciplines

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