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This is the same reason systems with a finite number of states cannot be chaotic Without more information, I don't think this is true. It is true if the transi
by dbaupp 14y ago
This is the same reason systems with a finite number of states cannot be chaotic
Without more information, I don't think this is true. It is true if the transition function between states depends on a finite number of previous ones (WLOG if s_n is a function of only s_{n-1}), but I think that it isn't if the transition depends on an infinite number.
(Though, in this case, clearly there is no history, so what you say is true.)
- eru 14y agoIf your model only depends on at most a maximum fixed length of history, you can always model your finite systems to only depend on the most recent state. (Just make a copy of the history part of that state.) In the case of depending on up to an infinite history, I wouldn't call that system to have a finite number of states any longer.