nonlinear dynamics 1 & 2: geometry of chaos
An advanced introduction to nonlinear dynamics, with emphasis on methods used to analyze chaotic dynamical systems encountered in science and engineering.
- course homepage: click here
- sign up here: piazza.com/gatech/spring2015/phys7224
use your email (no need for Georgia Tech email address) together with access code phys7224
And do sign up, even if you do not intend to do the homeworks - following the chatter on the course forum you might inadvertently learn something that your professor does not know.
what is this course about?
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
- Transfer operators - statistical distributions in dynamics
- Spectroscopy of chaotic systems
- Dynamical zeta functions
- Dynamical theory of turbulence
why this course
Most institutions have too few graduate students in any narrow specialty to offer a high level specialized course tailored to them. This Specialized Open Online Course is an experiment in sharing such advanced course with the off-campus research cohort. [A longer blurb]
A basic background in linear algebra, calculus, ordinary differential equations, probability theory, classical and statistical mechanics: ability to work with equations involving vectors and matrices, differentiate simple functions, and understand what a probability distribution is. Weekly homework assignments require both analytic and numerical work, so we will teach you Python as we go along. Knowledge of Matlab or Octave or another programming language is a very helpful. For introductory literature, check the book. You might want to take a preparatory course first.
We are grateful to the family of late G. Robinson, Jr. and National Science Foundation, grant DMS-1211827 for support