Nonlinear Dynamics 1: Geometry of Chaos

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

About The Course

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 (this course)
  • 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 (second course)
  • 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.

Frequently Asked Questions

Can I get a Statement of Accomplishment after completing this class?
Yes. Students who successfully complete the class can receive a Statement of Accomplishment signed by the instructors.

What resources will I need for this class?
An internet connection, python 2.7 (downloadable for free from website)

What background is expected for learners in this class?
Prior knowledge of linear algebra, calculus, differential equations, a strong drive to learn and an inquisitive mind. For more detail, read this.

Recommended Background

Familiarity with basic concepts in linear algebra, calculus, and probability theory. Specifically, ability to understand simple equations involving vectors and matrices, differentiate simple functions, and understand what a probability distribution is. For the exercises, some familiarity with Matlab or Octave would be helpful.