You really show that chaos is beautiful. Must have taken quite some time.
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It did take time! Probably spent five or 10 minutes drawing and labeling different parts of the diagram, and erasing mistakes, and even with that, you can probably still spot a few errors. I hope the students liked the slow process as much as I did. It was fun but scary
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Now I'm curious.
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An introduction is given at the following link, but without the manifold picture I drew on the board, and without Melnikov’s main clever calculation: https://en.m.wikipedia.org/wiki/Melnikov_distance?wprov=sfti1 …
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Are you by any chance familiar with DYNAMICS: THE GEOMETRY OF BEHAVIOR, by Abraham & Shaw? It aims to teach the subject using only pictures (i.e., without equations.) Fascinating effort, both mathematically and pedagogically. One senses that Rene Thom would have approved.
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I greatly admire those four volumes by Abraham and Shaw and learned a lot from them when I was just starting out in dynamical systems. In fact, I borrowed a few figures from them for my nonlinear dynamics textbook! (With permission and attribution, of course)
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I can't believe how well drawn those are. Math and art are one.
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Thanks Sinan!
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Those are some beautiful diagrams! I bet you must have practiced drawing them by hand copiously before doing them live in front of a classroom
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Ummmm. Honestly, I didn’t. I should have! I did them very ponderously, and the class helped me a lot :-)
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