Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site redwood.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!ihnp4!zehntel!dual!amdcad!fortune!rhino!redwood!rpw3 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 UUCP: {ihnp4,ucbvax!dual}!fortune!redwood!rpw3 DDD: (415)572-2607 USPS: 510 Trinidad Lane, Foster City, CA 94404