Re: basins of attraction

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#896

From: Tom Scavo
Date: Mon, 28 Dec 1992 17:23

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In article <erwin.725499996@trwacs> erwin@trwacs.fp.trw.com (Harry Erwin) writes:
>The basin of attraction for an attractive fixed point is the region that
>converges on the point under the operation of the function. Look at the
>inverse of the function. The region that nearby points reach under the
>operation of the inverse is the basin you're looking for.

Conceptually maybe, but is this practical?  Consider the following example:

The map  F(x) = x - tan(x)  has a third order attracting fixed point
at  x = pi .  The immediate basin is, I believe, bounded by a repelling
2-cycle.  How do I get a handle on this basin numerically?

>Note that if the
>function operates discretely, the resulting "basin" may well be quite
>strange...

I'd be happy with the _immediate_ basin (which is an open interval).

-- 
Tom Scavo
scavo@cie.uoregon.edu

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From: scavo@cie.uoregon.edu (Tom Scavo)
Newsgroups: sci.math.num-analysis
Subject: Re: basins of attraction
Summary: Here's a simple example...
Keywords: iteration basin attraction algorithm
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Date: 28 Dec 92 17:23:38 GMT
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