Math 145, Chaos Theory, Spring 2017

Week 1, 1D Iterations

• Articles
  • MS#97, Stairway to Chaos
  • MS#98, Complex Dynamical Systems
  • MS#142, Chaos Theory and the Tragedy of the Commons
  • Point set topology, brief PDF from Foundations of Mechanics
  • Annotated bibliographies by RA
• Books
  • Dynamics: The Geometry Of Behavior, RA, Shaw, 1992.
  • Chaos in Discrete Dynamical Systems: A Visual Introduction in 2 Dimensions, RA, Gardini & Mira, 1997.
  • The Chaos Avant-Garde: Memoirs of the Early Days of Chaos Theory, RA, Ueda, 2000.
  • Devaney, Robert L., Chaos, Fractals, and Dynamics: Computer Experiments in Mathematics, Addison-Wesley, 1990.
  • Pilkey, Orrin H., and Linda Pilkey-Jarvis, Useless Arithmetic: Why Environmental Scientists Can't Predict the Future, Columbia University Press, 2007.

Week 2, 2D Iterations

• Articles
  • Two-dimensional iterations. H. A. Lauwerier. Ch. 4 in Holden, 1996.
  • Complexity in business cycle models, H. A. Lorenz. Ch 2 in Gori, 1993.
• Books
  • Chaos in Discrete Dynamical Systems, Abraham, Gardini, and Mira, 1997.
  • Chaotic Economic Dynamics, Richard M. Goodwin, 1990.
  • Nonlinear Dynamics in Economics and Social Sciences. F. Gori, L. Geronazzo, M. Galeotti, eds, 1993.
  • Arun V. Holden, ed. Chaos, 1986.

Week 3, 1D and 2D Flows

• Books
  • Dynamics, the Geometry of Behavior, Abraham and Shaw, 1992. (Secs. 1.6, 2.1, 3.1, 3.3)
  • Nonlinear Dynamics and Chaos, Strogatz, 1994.
  • JavaScript: the Good Parts, Crockford, 2008

Week 4, 3D Flows and Chaos

• Books
  • Dynamics, the Geometry of Behavior, Abraham and Shaw, 1992. (Chs. 4 and 8)
  • Nonlinear Dynamics and Chaos, Thompson and Stewart, 1986. Unique source for the Ueda and Shaw attractors.
  • Equations for some flows, 2D and 3D

Week 5, 3D Flows and Chaos

• Books
  • Dynamics, the Geometry of Behavior, Abraham and Shaw, 1992. (Chs. 10 to 15)
  • The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors, Colin Sparrow, 1982. Exhaustive source for the Lorenz attractor.

Week 6, Cybernetics, economics

• Websites: Macy conferences, McCulloch and Pitts, Richard M Goodwin

Week 7, System dynamics

• MS# 98, 108, 139

P5 Programming

• p5.js website
• Ryan Drury's flow app

Software Help

• UCSC ITS (SFTP, FileZila)
• UCSC ITS (Personal web pages)
• Atom (free) or Smultron ($10) (Code editor for Mac)
• For editing code under Windows, check out Atom and Notepad++.