Complexity Explorer Santa Fe Institute

This course is no longer in session.
Bifurcationdiagram

Introduction to Dynamical Systems and Chaos (Fall, 2017)

Lead instructor:

Course Videos and Other Materials (zip files):

These zipped files contain all course materials for the given unit except for the homework solutions.

 

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.  amazon.com
  • 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.  amazon.com
  • Mitchell, Melanie. Complexity: a guided tour. Oxford University Press, 2009.  A general book about complex systems.  amazon.com

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.  amazon.com
  • Smith, Peter. Explaining chaos. Cambridge University Press, 1998.  More technical than Kellert.  amazon.com

  • 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.  html

  • 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.  amazon.com

  • 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.  amazon.com

  • Sayama, Hiroki, Introduction to the Modeling and Analysis of Complex Systems.  OpenSUNY Textbooks.  Looks like a great survey of a range of topics in complex systems, including dynamical systems.  A pdf is available here.

  • 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.  amazon.com

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

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

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

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

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

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.   dailymotion.com  vimeo.com (with arabic(?) subtitles)
  • Jos Leys, Etienne Ghys, and Aurelien Alvarez, Chaos: A Mathematical Adventure.  A set of videos availalbe in 11 different languagues.   http://www.chaos-math.org/en.
  • Steven Strogatz, Nonlinear Dynamics and Chaos.  A series of 25 lectures from the course MAE5790 at Cornell University in Spring 2014.  The lectures closely follow Strogatz's textbook, listed above.  youtube.com