Oh, the pleasures of teaching Melnikov’s method! Drawing the manifolds in real time is very stressful, but funpic.twitter.com/p7sdJXnz3p
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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)
That is a very beautiful book. It should really be more well known. Currently you can only buy it directly from the author.
"Pictures have eyes." I always told students in my math and physics classes that they would be able to solve a problem if they could draw a diagram for it. In fact, final exam solutions for my undergrad ODE class was just two pages of diagrams! No messy, boring computations.
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