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Unformatted text preview: n rotational symmetries in the plane together with the n reection symmetries form a group that is isomorphic to D n . See Exercise 2.3.10 . Figure 2.3.3 (below) has D 9 symmetry, while Figure 2.3.4 possesses Z 5 symmetry, but not D 5 symmetry. Both of these gures were gener-ated by several million iterations of a discrete dynamical system exhibit-ing chaotic behavior; the gures are shaded according to the probability of the moving particle entering a region of the diagram the darker regions are visited more frequently. A beautiful book by M. Field and M. Golubitsky, Symmetry in Chaos (Oxford University Press, 1992), discusses symmetric gures arising from chaotic dynamical systems and displays many extraordinary gures produced by such systems....
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- Fall '08