Contemporary Mathematics 252 (1999) 63-70.
Abstract
This note provides an accessible family of examples, based on Newton's method that exhibit chaotic dynamics. We show this by establishing that the dynamics is transitive and by finding an exact formula for Lyapunov exponents. A somewhat unexpected consequence of this study is that periodic orbits seems to lose their instability in a singular way.
AMS Classification Codes: 28D05, 34D08
Keywords: Newton's method, Lyapunov exponents, chaotic dynamics.