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From: rpw3@redwood.UUCP (Rob Warnock)
Newsgroups: net.physics
Subject: Re: Re: Non-linear systems.
Message-ID: <115@redwood.UUCP>
Date: Sun, 13-Jan-85 02:17:21 EST
Article-I.D.: redwood.115
Posted: Sun Jan 13 02:17:21 1985
Date-Received: Sun, 20-Jan-85 07:54:31 EST
References: <209@talcott.UUCP>, <328@rlgvax.UUCP> <384@hou2g.UUCP>, <1027@sunybcs.UUCP> <386@hou2g.UUCP>
Organization: [Consultant], Foster City, CA
Lines: 30

+---------------
| For many non-linear systems, infinitesimally different states at t=0 can
| be arbitrarily "far apart" at t=T...  | Jim | ihnp4!hou2g!stekas
+---------------

In fact, it should be possible to construct a system which is "arbitrarily
non-linear everywhere", to coin a phrase. That is, given some time T and
some epsilon E > 0 (no matter how small) and delta D (no matter how large),
one should be able to construct systems S(s0,t) for which, given two initial
states s1 and s2 such that the initial states are at least E apart (according
to whatever convenient metric ||x-y|| you choose):

	|| S(s1,0) - S(s2,0) || > E

the states at time t > T  are farther apart than D:

	|| S(s1,t) - S(s2,t) || > D

I remember some constructions we did in math in college many (many!) years
ago with functions that were "discontinuous everywhere". Has the above
sort of thing been done with physical systems? Is this the sort of stuff
Catastrophy Theory is supposed to deal with?


Rob Warnock
Systems Architecture Consultant

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