MLA 31500
Natural Sciences
Elective
Order and Chaos in the Natural World
Spring Quarter 2008
CLASS NOTES
THIRD CLASS
April 12, 2008
I. STEWART, CHAPTER 6: STRANGE ATTRACTORS
1. What is the essential question about the behavior of dynamical systems that is addressed in this chapter? What is the answer for a two-dimensional system (i.e., for motion in a plane)?
2. Stewart also explains that Smale began with an incorrect conjecture. What is the essential content of that conjecture as portrayed by Stewart?
3. In what sense does the analysis of the van der Pol oscillator (Stewart, pp. 91-92, 137) constitute a mathematical proof that SmaleÕs conjecture is wrong?
4. What is the physical system represented by the solenoid constructed on pages 106-109? What are the physical laws that underlie the equations governing the behavior of that system?
II. STEWART, CHAPTER 8: RECIPE FOR CHAOS
1. What is the physical system represented by the SmaleÕs horseshoe constructed on pages 137-139? What are the physical laws that underlie the equations governing the behavior of that system?
2. What aspects of chaotic behavior are represented or modeled by SmaleÕs horseshoe?
3. We shall discuss the Henon-Heiles model and the Henon map on May 3.
4. We shall discuss the logistic map on May 10.
LINKS:
Return to Course Page; mla315spring2008.htm
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Page: pov.html
Go to the home page of the Department of Astronomy and Astrophysics
of the University of Chicago: http://astro.uchicago.edu/