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I'm looking for a differential-geometry based exposition of chaos theory and quantum chaos. Ideally, it would start with the Hamiltonian formalism (on symplectic manifolds) and discuss as many of the following as possible:

  1. Liouville integrable systems
  2. "orbits" of a system
  3. definitions of when a system is mixing/chaotic/"Anosov"
  4. mathematical formulation of correspondence principle (Egorov theorem)

Perhaps it would be somewhat like the book Chaos in Classical and Quantum Mechanics by Martin C. Gutzwiller, only more formal and focusing on quantum chaos.

I would love to look at any references that are even tangentially related. Thanks in advance!

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"Quantum Chaos - between order and disorder" Casati and Chirikov (no differential geometry)

"Foundations of Mechanics" Ralph Abraham and Jerry Marsden - (plenty of differential geometry) - classical mechanics +

"A first Course in Dynamics" - Anatole Katok - Ergodic theory

I'm sure there are many others, perhaps a few more suggestions would help.

Oh, Predrag Cvitanovic , "Chaos: Classical and Quantum" , website: ChaosBook.org

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    $\begingroup$ Thanks for the references. Alas, only Abraham and Marsden's textbook seems to be at the level of rigor I'm looking for, but they deal only with classical mechanics (and not about chaotic systems/quantization)... $\endgroup$ – user117824 Dec 27 '13 at 4:47

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