UCSC: Porter 34B, Chaos, Fractals, and the Arts, Winter 2005

Agenda for Meeting #4, 27 Jan 2005

• 2A, Quiz #2 (15 minutes)
• 2B, Ralph (90 minutes):
  • Results of Quiz #1, Chops histogram, Xsection Sat
  • Discuss Chs. 1-3 of Bolts
  • Stairway to chaos, continued
    • Review of 1D, Lab #1, #2
    • Concepts of chaos theory: 2D maps
    • Describe software for chaos lab #3 homework

  HW for Meeting #5

  • Short essay on Ch. 3, algebra
  • Read Ch. 4, Dante and Fra Angelico
  • Chaos exercizes (hand in lab notes) applet: Dorband (double logistic) map family
  • Suggestions:
    • Describe all attractors you can find, for c = 0.1.
    • Ditto for c = 0.5, 0.6, and 0.7.

  References

  Chaos in Discrete Dynamical Systems

  Optional reading, online (PDF) text by ralph and others

  Part I (Chs. 1-3) gives a low-level intro to the concepts of iterated maps, 1D and 2D

  Ch. 7 (not online) is an exhaustive analysis of the Dorband family.

  See also, Abraham MS#69 (not online)

  Twisted double logistic map (with Gardini, Record, and Prunaret), Int. J. Bifurcations and Chaos, 4(1), Feb., 1994.

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  Revised 24 Jan 2005 by Ralph