General Information
Class and Exams Schedule
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General Information
- Textbook: Nonlinear
Dynamics and Chaos by Steven H. Strogatz. Publisher: Westview
Press.
- Supplemental textbook: A first course in chaotic dynamical systems
by Robert L. Delaney. Publisher: Addison Wesley
- Suggested reading (global
popular science overview):
- The essence of Chaos
by Edward N. Lorenz. Publisher: University of Washington Press
- Chaos: Making a new Science
by James Gleick. Publisher: Penguins Book
- The Beauty of Fractals by
Heinz-Otto Peitgen and Peter H. Richter. Publisher: Springer-Verlag
- Eligibility:
- AMS 27, or MATH 27, or MATH 21 and 24.
- Homework: Suggested homework will be given every week and
answers will be discussed in Section. You are strongly advised to
attempt and complete as much of the homework as possible and go to
section to find out the correct answers. Homework is not graded.
- Quizzes: Will be held approximately every two weeks and
will usually be based on one of the homework problems set during the
previous two weeks.
- Exams: There will be one mid-term exam and a final project
(no final exam).
- Grading Policy:
- Quizzes: 30 % of total grade.
- Mid-term: 30 % of total grade.
- Final project: 40 % of total grade.
Tentative Schedule: (this will be updated as
the
course progresses)
- Week 1 (March):
- Mar 29: General introduction to Dynamical Systems and Chaos
- Mar 31: Flows on the line (Chapter 2)
- Week 2 (April):
- Apr 5: Bifurcations part 1: Saddle-nodes and transcritical
bifurcations. Normal forms. (Chapter
3.1, 3.2)
- Apr 7: Bifurcations part 2: Pitchforks. Example of the
bead on a hoop. Imperfect bifurcations.
Notion of co-dimension. (Chapter
3.4, 3.6)
- Week 3:
- Apr 12: Quizz 1. Applications of continuous 1D systems:
Population dynamics
- Week 4:
- Apr 19: Introduction to 2D systems. Fixed points and
linearization
- Apr 21: Solution of linear systems. Classification of fixed
points.
- Week 5:
- Apr 26: Examples of 2D systems. The nonlinear pendulum, the
nonliear damped pendulum and the predator prey model.
- Apr 28: Structural stability of fixed points. Example of the
predator-prey model. Conservative and
reversible systems (Chapter 6.5).
- Week 6 (May):
- May 3: Limit cycles (Chapter 7)
- May 5: Bifurcations in 2D systems. Example of the solar
dynamo
- Week 7: (also based on supplemental textbook)
- May 10: One-D Maps part 1
(Chapter 10.1, 10.2)
- May 12: The Logistic Map in detail; Universality and
Period Doubling route to Chaos. (Chapter
10.4, 10.7)
- Week 8:
- May 17: Definition of Chaos.
Lyapunov exponents; examples. The Tent Map
- May 19: Midterm
- Week 9:
- May 24: From dynamical systems to Fractals. Example: the Tent
Map. Definition of Fractals.
- May 26: 2D maps
- Week 10: (May-June)
- May 31: Fundamental examples of
dynamical systems: 1. the restricted 3-body problem
- Jun 2: Fundamental examples of
dynamical systems: 2. The Lorenz
equations