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From: scavo@cie.uoregon.edu (Tom Scavo)
Newsgroups: comp.theory.dynamic-sys
Subject: Re: Can Chaos Be Predictable?
Keywords: chaos, predictability
Message-ID: <1991Jun21.153833.24881@ariel.unm.edu>
Date: 21 Jun 91 15:38:33 GMT
Article-I.D.: ariel.1991Jun21.153833.24881
References: <1991Jun20.194552.15875@cunews.carleton.ca>
Distribution: comp.theory.dynamic-sys
Organization: Campus Information Exchange, University of Oregon
Lines: 20

In article <1991Jun20.194552.15875@cunews.carleton.ca> rdb@scs.carleton.ca (Robert D. Black) writes:
>I recently read that the chaotic logistic equation
>
>    u(t+1) = 4u(t)(1-u(t))      u(0) in 0..1,
>                                t = 0,1,2,...
>has an ANALYTIC SOLUTION: 
>
>    u(t) = sin**2 (2**(t-1) arccos(1-2u(0)))
>
>    Reference "Differential Equations" by Walter G. Kelly and
                ^^^^^^^^^^^^
>    Alan C. Peterson, Academic Press 1991, p184.

A small correction:  the title of the referenced book is
"Difference Equations" which can be guessed by the above
example.  Just wanted to set the record straight...

-- 
Tom Scavo
scavo@cie.uoregon.edu