There is a post by Mark at Cosmic Variance requesting ideas for topics for a course on mathematical physics. I added a comment suggesting non-linear dynamics for storage rings could make a good topic.
Thinking it through a bit more, perhaps this would be tough. I myself am in the process of trying to understand this field better and pick out what is and isn't essential. So maybe its not ready for someone to pick up outside the field.
The references I mentioned were to Dragt's online book and to the book by L. Michelotti called “Intermediate Classical Dynamics with Applications to Beam Physics”. The wikibook might still be a good place to sort this out.
Perhaps if one is talking about Lie Algebras or Lie Groups, this is nice to know that they are not just used in particle physics, but in classical mechanics as well. And classical mechanics is such a broad subject. It is almost the same as mathematical methods of classical systems.
I also mentioned that the maps with their resonance islands and separatrices and chaotic and non-chaotic regions had made their way into atomic and molecular physics through the quantum accelerator modes. Here is a link, first from google, but I haven't looked into the field enough to judge it yet... A topic for more investigation. I do know that the name of Shmuel Fishman comes up a lot with respect to this research area.
(Added comment: This topic did make it into several articles in Journal of Mathematical Physics. For example, see an article by Forest here.)
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