Re: question about ODEs and processes they describe

From: Justin Davis (jkd3_at_duke.edu)
Date: 06/13/04 

Date: Sun, 13 Jun 2004 15:37:16 GMT

"Alexander Korovyev" <korovyev@rambler.ru> wrote in message
news:26c82787.0406130553.6b5a4a8a@posting.google.com...
> From the very beginning of my course on ordinary differential
> equations I was told that this theory helps to describe and study
> finite-dimensional, deterministic and differentiable processes. The
> state of such a process is a point of a so-called phase space and at
> any given time-point fully describes the process' present, past and
> future. So the process' evolution (phase trajectory) is identified
> with a smooth curve in a differentiable manifold (phase space). Since
> every state must determine some phase trajectory (process' past,
> present and future relative to the state's time-point), phase
> trajectories clearly must not intersect. Ok, so far so good. But what
> about ODE of this kind: dx/dt = x^(2/3)? How many parameters are
> needed to characterize a state of a process described by this ODE? It
> looks like the phase space is 2-dimensional but it is not! Suppose the
> process starts at x = 0, is it possible to tell its evolution? What
> information do we need for this? Was I told a lie that all ODEs
> describe finite-dimensional, deterministic and differentiable
> processes? I'd be happy to hear any clarification on this issue.
> Thanks.

"This theory helps to describe and study finite-dimensional, deterministic,
and differentiable processes" does not imply that "all ODEs describe
finite-dimensional, deterministic and differentiable processes" in the same
way that "water helps to put out fires" does not imply that "all water is
used to put out fires." Not sure why it was necessary to include the idea of
a "lie." Sorta antagonistic.

If your system starts at x = 0, why would it move, since at that point,
dx/dt = 0?

Relevant Pages

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  • question about ODEs and processes they describe
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  • question about ODEs and processes they describe
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