No CrossRef data available.
Article contents
How many real attractive fixed points can a polynomial have?
Published online by Cambridge University Press: 14 February 2019
Extract
While the notion of roots of a quadratic polynomial is rudimentary in high school mathematics, that of its fixed points is uncommon. A real or complex number is a fixed point of a polynomial p (x) p (θ) = θ. The fact that the notion of fixed point of polynomials is not commonly covered in high school or undergraduate mathematics is surprising because the relevance of the fixed points of a quadratic can be demonstrated easily via iterative methods for the approximation of such numbers as 
, when the quadratic formula offers no remedy.
- Type
- Articles
- Information
- Copyright
- Copyright © Mathematical Association 2019
References
1. Devaney, R. L., A first course in chaotic dynamic system theory and experiment (ABP) (1992).Google Scholar
2. Mandelbrot, B. B., Fractal geometry of nature, W. F. Freeman, New York (1993).10.21236/ADA273271Google Scholar
3. Kalantari, B., Polynomial root-finding and polynomiography, World Scientific, Hackensack, NJ (2008).10.1142/6265Google Scholar
4. Beardon, A. F., Iteration of rational functions: Complex analytic dynamical systems, Springer-Verlag, NY (1991).10.1007/978-1-4612-4422-6Google Scholar
5. Milnor, J., Dynamics in one complex variable: Introductory lectures, Vol 160 (3rd edn.) Princeton University Press, NJ (2006).Google Scholar
6. Burden, R. L., Faires, J. D., Numerical Analysis, Brooks Cole, Pasicif Grove, CA (2004).Google Scholar