Math 333
Chaotic Dynamical Systems
Spring 2008
Time: Tuesday and Thursday, 6:00 -- 7:15 pm
Place: LD 002
Textbook: A First
Course in Chaotic Dynamical Systems, Theory and Experiment, by
Robert L. Devaney
Instructor: Michal Misiurewicz
Office: LD 224F
Phone: 274-8101
E-mail:
mmisiure@math.iupui.edu
Office Hours: Tuesday 2:00 - 4:00 pm and
Thursday 10:00 am - 12:00 noon
Student Audience: This is a course for students
majoring in Mathematics, Science and Engineering.
Prerequisite: The prerequisite for this course is
completion of MATH 164 or MATH 222 (or equivalent) within the past
three years with a minimal grade of C.
Computer experiments: JAVA applets that accompany
the book are posted at the Web here
(look for applets associated with the book Chaos).
Course objectives: Students should understand the
basic notions of Dynamical Systems and be able to use them in solving
problems and performing numerical experiments.
Course outline: The following subjects will be
covered (if time allows):
- Orbits of dynamical systems
- Graphical analysis
- Fixed and periodic points
- Bifurcations
- Quadratic family
- Transition to chaos
- Symbolic dynamics
- Chaos
- Sharkovsky's Theorem
- Role of the critical orbit
- Newton's method
- Fractals
- Julia and Mandelbrot sets
Grading policy: Each week there will be homework
assigned, to be submitted for grading. The homework scores will
constitute 70% of the total score. There will be also a take-home
final examination. The final exam score will constitute 30% of the
total score.
You need approximately 80% of the maximum possible score for A-,
66.7% for B-, 53.3% for C-, and 40% for D-.
Final Examination: Take-home, due Tuesday, April 29.
Withdrawal deadline: March 28. Details can be found
here.
Homework assignments:
- Page 34, exercise 4 c, d, f, and exercise 5 - for January 22
- Page 67, exercise 1 c, d, g - for January 29
- Page 80, exercises 10, 11, 13 - for February 5
- Page 95, exercises 12, 13 - for February 12
- Page 113, exercise 18 d, e, f, g, h - for February 19
- Page 131, exercises 8, 9, 10, 11 - for February 26
- Page 152, exercise 9 - for March 4
- Page 163, exercise 10 c, d - for March 18
- Explain the behavior of the trajectories for the Newton's method
for the function used in this applet:
http://www.math.umn.edu/~garrett/qy/BadNewton.html - for March 25
- What IFS leads to a picture like in Figure 14.19 (b), page 198? -
for April 1
- The same question for Figure 14.18 (a), (b) and 14.19 (a), (c)
[for extra credit] - for April 8
- Page 219, exercise 8 b, f, g [regular homework] - for April 8
Mortgage calculation is here.
Orbit diagrams for quadratic and cos families of maps; a graph of a cos map.
Last updated: April 1, 2008
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