nordita master class in physics 2015 : geometry of chaos

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

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what is this course about?

The theory developed in the full online course (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.

Nordita Master Class in Physics 2015: Geometry of chaos (see syllabus)

Topology of flows - how to enumerate orbits, Smale horseshoes
Dynamics, quantitative - periodic orbits, local stability

prerequisites

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.

format

Nordita master class in physics 2015 covers roughly 4 weeks of the full online course and consists of book study, with links to explanatory videos, and homework assignments, which include some computer programming. While you are free to use any computational tool that you are comfortable with, we are going to provide you Python script templates for computational assignments.

textbook

The course is based on P. Cvitanović et al. ChaosBook.org. In the first 8-week online course we will cover Part I of the book, or most of the material from chapter to "Flows" to "Fixed points, and how to get them". Your active participation in improving the book is very much appreciated.

instructor

Predrag Cvitanović Georgia Institute of Technology

We are grateful to the family of late G. Robinson, Jr. and National Science Fundation, grant DMS-1211827 for support