On continuous descent functions for polynomial equations

• DOI: 10.1007/bf01595136
• Publication Date: 2005-04-28T19:42:59Z
• Authors: Duncan H. Martin
• Keywords: Descent (aeronautics)

In his recent book, Henrici (1974) gave an axiomatic treatment of the method of descent applied to the solution of polynomial equations, dealing in particular with the non-existence of continuous descent functions defined on the whole complex plane. This note presents an alternative account of this question, in which a somewhat stronger theorem is proved. At the same time, a certain problematical step, to which Henrici himself drew attention, is avoided.