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 I: Geometry of chaos
- Topology of flows - how to enumerate orbits, Smale horseshoes
- Dynamics, quantitative - periodic orbits, local stability
- Role of symmetries in dynamics
Nonlinear dynamics II: Chaos rules
- Transfer operators - statistical distributions in dynamics
- Spectroscopy of chaotic systems
- dynamical zeta functions
- Dynamical theory of turbulence
The course is in part an advanced seminar in nonlinear dynamics, aimed at PhD students, postdoctoral fellows and advanced undergraduates in physics, mathematics, chemistry and engineering.