The theory developed here (that you will not find in any other course 🙂 has much in common with (and complements) statistical mechanics and field theory courses; partition functions and transfer operators are applied to computation of observables and spectra of chaotic systems.
Nonlinear dynamics 1: Geometry of chaos (see syllabus)
Topology of flows – how to enumerate orbits, Smale horseshoes
Dynamics, quantitative – periodic orbits, local stability
Role of symmetries in dynamics
Nonlinear dynamics 2: Chaos rules (see syllabus)
Transfer operators – statistical distributions in dynamics
Spectroscopy of chaotic systems
Dynamical zeta functions
Dynamical theory of turbulence
The course, which covers the same material and the same exercises as the Georgia Tech course PHYS 7224, is in part an advanced seminar in nonlinear dynamics, aimed at PhD students, postdoctoral fellows and advanced undergraduates in physics, mathematics, chemistry and engineering.
An interesting looking online course that appears to be on a white-labeled Coursera platform.
I’ve come across Predrag Cvitanovic’s work on Group Theory and Lie Groups before, so this portends some interesting work. I’ll have to see if I can carve out some time to sample some of it.