Fibonacci-type polynomial as a trajectory of a discrete dynamical system |
| |
Authors: | Mattew X He Davis P Simon Paolo E Ricci |
| |
Institution: | (1) Department of Mathematics, Nova Southeastern University, 33314 Ft. Lauderdale, FL;(2) Dipartimento di Matematica Guido CASTELNUOVO, Università degli Studi di Roma La Sapienza, Italy |
| |
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
byQ
2. The starting point for each trajectory is fixed byR
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-calledr-Bonacci polynomials. |
| |
Keywords: | AMS classification" target="_blank">AMS classification 12E10 30C15 |
本文献已被 SpringerLink 等数据库收录! |
|