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Conversely given a discrete dynamical system you can build a /higher-dimensional/ continuous system with a Poincare section that gives the discrete system back! So all the chaos you see in discrete evolutionary models will happen in higher dimensional continuous models too.
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The basic way to build a continuous system from a discrete is the /mapping torus/ -- if your discrete system is f: X-> X, you take X x [0,1]_t, glue Xx0 to Xx1 using f, and flow in the t direction! This is a basic mathematical construction that more folks should know!
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Now [0,1] with 0 glued to 1 is the circle, which sits in the plane. So if f: R -> R was your discrete 1d dynamical system (evolutionary model) then i can build a 3d continuous dynamical system with the same amount of chaos as your 1 d system ;) Thus Poincare-Bendixon fails in 3d!
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In general the relation between dimension and `complexity' is amazing. An incredible theorem of Kozlovski et al shows that Axiom A systems -- ones which behave topologically like nondeterminstic finite state machine -- comprise most discrete dynamical systems in dim 1! Annals '07
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On the other hand there *exist* 2d discrete dynamical systems which are computationally universal in the sense that one can encode a Turing machine into their dynamics. I should dig up the reference -- ask if you are curious! So complexity goes up fast with dimension :-)
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So the moral is: Laura acutely observed an amazing thing, coming from an important theorem, but the discrete/continuous dichotomy is an illusion if you give yourself more dimensions to play with. And the world is very high dimensional!
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I know nothing about the literature! Intro me to good folks someday :-) I just see this construction as a way to see that in terms of `complexity', D-dimensional discrete dynamics ~ D+1-diml continuous system w topology ~ D+2 diml continuous system w/o topology
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