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.
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