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:
- Liouville integrable systems
- "orbits" of a system
- definitions of when a system is mixing/chaotic/"Anosov"
- 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!