Re: Which theorem proves that every chaotic system exhibits predicable

On Jan 7, 8:00 am, Shubee <e.Shu...@xxxxxxxxx> wrote:
I recall hearing of a very interesting theorem ages ago. I believe it
was in Ergodic theory. I believe that the theorem proved that every
chaotic system exhibits predicable behavior. Does that theorem have a
name?

Just guessing here, but you may be talking about the Poincare
recurrence theorem. It states that for a volume preserving dynamical
system, if a trajectory is confined to a finite volume, then after a
long enough time the trajectory will come arbitrarily close to its
initial point.

For example, if a chaotic system is Hamiltonian, Liouville's theorem
implies volume conservation. If the system also possesses a conserved
quantity, such as energy, which confines a given trajectory to a
compact hypersurface, the second hypothesis of the theorem is also
satisfied.

Hope this helps.

Igor

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