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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