Talk:Dynamical system (definition)
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I have created this article from the definitions that were added to the Dynamical system page. I modified the definitions of the smooth cases to use a manifold as the state space. I also moved Linas' measure theoretic definition to this page. — XaosBits 20:11, 15 October 2006 (UTC)
The claim that cellular automata are not dynamical systems because they are not invertible is a contentious one. Dynamical systems need not be invertible, although some of them are. See, e.g. "Introduction to the Modern Theory of Dynamical Systems" by Katok & Hasselblatt, Chapter 0, p2:
For a reversible system the transformations phi_t are defined for both positive and negative values of t and each phi_t is invertible. (My emphasis)
- i.e. dynamical systems, including cellular automata, need not be reversible. 139.184.30.17 16:48, 19 October 2006 (UTC)
I would like to add a section to show how a evolution function could be constructed, with particular emphasis on the physical origins of the concept and its relations to engineering applications. Is there any problem? Any criticism is welcome. :) Daniele Tampieri 11:45, 26 November 2006
[edit] Definition of I(x)
193.204.253.144 14:10, 16 January 2007 (UTC)The current definition of I(x) is not very meaningful. 
, as 
is comprised of all the possible pairs in which the first element is in T and the second in M, so basically couldn't we simply write that I(x): = T?
