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Unformatted text preview: explicitly) to show that { H, I 2 x + I 2 y } = 0 and {L , I 2 x + I 2 y } = 0 , i.e. H , L , and I 2 x + I 2 y are three (independent) integrals of the motion whose Poisson bracket vanishes. Project ideas 1. Numerically explore chaos in the fourvortex problem ( i.e. draw Poincar e maps, (maybe) Melnikovs method, . ..). 2. Look at the existence of relative equilibria in the Nvortex problem. 3. Compute LCS for problems in chaotic advection. 1...
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