An advanced, semester length introduction to nonlinear dynamics, with emphasis on methods used to analyze chaotic dynamical systems encountered in science and engineering.

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

    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 (second course)

    Transfer operators - statistical distributions in dynamics
    Spectroscopy of chaotic systems
    dynamical zeta functions
    Dynamical theory of turbulence

The course is aimed at PhD students, postdoctoral fellows and (very) advanced undergraduates in physics, mathematics, chemistry and engineering.