Newton's Method for Quadratics, and Nested Intervals

A bstract . The function h (z ) = ~ (z l i z ) is t he ewton map associated with the quadratic polynomial z 2 +1. The iterated dynamics of f on 3{ is usually st udied by exploit ing the conjugacy between f and the funct ion z f-> z2 In this paper we show how to use the technique of nested intervals t o yield a direct ana lysis of t he dynamics. We also show how to use the same technique to analyze t he dynamics of t he funct ion h(z) = z l i z .