Newton’s Method and Dynamical Systems

This article is devoted to the discussion of Newton's method. Beginning with the old results of A.Cayley and E.SchrOder we proceed to the theory of complex dynamical systems on the sphere, which was developed by G.Julia and P.Fatou at the beginning of this century, and continued by several mathematicians in recent years. Front Matter....Pages i-1 Newton’s Method and Complex Dynamical Systems....Pages 3-58 Discrete Versus Continuous Newton’s Method: A Case Study....Pages 59-80 The Continuous, Desingularized Newton Method for Meromorphic Functions....Pages 81-121 Global Aspects of the Continuous and Discrete Newton Method: A Case Study....Pages 123-202 Idiosyncratic Remarks by a Bibliomaniac: 5. A Random Sample of Structured Chaos....Pages 203-219 Book Review....Pages 221-226