Complexity Explorer Santa Few Institute

Introduction to Dynamical Systems and Chaos (Winter 2014)

Lead instructor:

This course is no longer in session.

Course Videos and Other Materials (zip files): (653 MB) (1 GB) (1.8 GB) (762 MB) (537 MB) (778 MB) (1 GB) (819 MB) (631 MB)


Additional Reading

non-technical:  these are books in the "popular science" style. 

  • Gleick, James. Chaos: Making a new science. Random House, 1997.  Very readable, focuses on the scientists and mathematicians behind many of the key results in chaos.
  • Stewart, Ian. Does God play dice?: The new mathematics of chaos. Penguin UK, 1997.  More mathematical  detail and richness than Gleick's book.  Also quite readable.
  • Mitchell, Melanie. Complexity: a guided tour. Oxford University Press, 2009.  A general book about complex systems.

history and philosophy of science: these books and articles are mostly non-technical, but are scholarly pieces on the history and philosophy of science. 

  • In the Wake of Chaos: Unpredictable Order in Dynamical Systems.  Stephen H. Kellert.  University of Chicago Press.  1994.
  • Smith, Peter. Explaining chaos. Cambridge University Press, 1998.  More technical than Kellert.

  • Aubin, David, and Amy Dahan Dalmedico. "Writing the History of Dynamical Systems and Chaos: Longue Durée and Revolution, Disciplines and Cultures." Historia Mathematica 29.3 (2002): 273-339.  A long paper thoroughly examining some of the strands of thoughts that converged to form the field of chaos and dynamical systems.  pdf

  • Bishop, Robert, "Chaos", The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.) html

  • Hoefer, Carl, "Causal Determinism", The Stanford Encyclopedia of Philosophy (Spring 2010 Edition), Edward N. Zalta (ed.)  html

textbooks with more mathematical details:  i've listed these textbooks in approximate order from introductory to advanced.

  • Feldman, David P. Chaos and Fractals: An Elementary Introduction. Oxford University Press, 2012.  At roughly the same level as this class.

  • Flake, Gary William. The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptations. The MIT Press, 1998.  In a few places uses calculus.  A very clear and engaging introduction to chaos, fractals, and complex systems more generally.

  • Kaplan, Daniel, and Leon Glass. Understanding Nonlinear Dynamics. Springer-Verlag, 1995.  A basic introduction to dynamical systems.  Uses calculus but does not assume prior coursework in differential equations.

  • Strogatz, Steven. Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering. Westview Press, 2001.  Highly recommended.

  • Peitgen, Heinz-Otto, Hartmut Jürgens, and Dietmar Saupe. Chaos and fractals: new frontiers of science. Springer, 2004.

  • Smale, Stephen, Morris W. Hirsch, and Robert L. Devaney. Differential equations, dynamical systems, and an introduction to chaos.  (3rd edition.) Academic Press.  2012.

  • Devaney, Robert L.  An Introduction to Chaotic Dynamical Systems. (2nd edition.)  Westview Press, 2003.

  • Ott, Edward. Chaos in Dynamical Systems. (2nd edition.) Cambridge University Press, 2002.

lectures and documentaries

  • Raymond Flood.  Butterflies, Chaos and Fractals.  Museum of London.  17 September 2013.  link
  • Nic Stacey and Jim Al-Khalili.  The Secret Life of Chaos.  BBC 4.  January 2010. (with arabic(?) subtitles)