Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site stolaf.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxl!ihnp4!stolaf!heathd From: heathd@stolaf.UUCP (Daniel J. Heath) Newsgroups: net.math Subject: complex convergences Message-ID: <1517@stolaf.UUCP> Date: Mon, 27-Feb-84 19:30:29 EST Article-I.D.: stolaf.1517 Posted: Mon Feb 27 19:30:29 1984 Date-Received: Sun, 4-Mar-84 02:55:10 EST Organization: St. Olaf College, Northfield MN Lines: 21 I recently encounterred this problem in the American Mathematics Monthly (Feb 1984, Vol. 91, No. 2, Proposed by F. Lazebnik, Univ Pennsylvania and Y. Pilipenko, Kiev Univ. USSR.): Define a sequence {a[n]} (where [n] is a subscript--rather hard to represent in type) such that a[1] = a and a[n+1] = a[n]^2-2. For what values of a does this sequence converge. It is with a fair amount of ease that I defined an infinite number of values that fulfill these stipulations. Lately, with all this talk of complex numbers, I came up with a similar, yet somewhat more difficult problem which I would like to propose to you math-masochists like myself. Given a sequence {a[n]} such that a[1] = a and a[n+1] = a[n]^2-2*i, are there values such that this sequence converges, and if so, what are they? Send any comments to me, I'll post them. deej !stolaf!heathd