Instructor: John Gemmer
Office: Manchester #388
E-mail: gemmerj@wfu.edu Office Hours: Tuesday 9-10, Wednesday 2:30-3:30, Thursday 1-3
Lecture: MWF: 9:00-9:50, Manchester 124
Textbooks: See syllabus.
Course Handouts:
1. Syllabus: (.pdf)
Mathematica Notebooks:
Matlab Scripts:
1. Constant slope on Tori (.m)
2. 2-d Kuramoto model (.m)
Lecture Notes:
1. Lecture #1: (Motion on Tori and Cylinders) (.pdf)
2. Lecture #2: (Some Properties of the Lorenz Equations) (.pdf)
3. Lecture #3: (Lorenz Map and Iterated Maps) (.pdf)
4. Lecture #4: (Fractals and Iterated Maps) (.pdf)
Homework Assignments:
1. Homework #1 (.pdf).
2. Homework #2 (.pdf).
3. Homework #3 (.pdf).
Potential Topics for Student Presentations:
1. Homework #1, Problem #1
2. Homework #1, Problem #2
3. Homework #1, Problem #4
4. Homework #1, Problem #5
5. Derivation of the Lorenz Model (.pdf).
6. Nonautonmmous Linear Systems and Floquet Theory (.pdf).
7. Gronwall's Inequality and Continuity of Solution Map for ODEs (.pdf).
8. Proof of Poincare Bendixon Theorem using Poincare Maps (.pdf).
9. Logistic Map (Numerical experiments, chaos and periodic windows). Sections 10.2-10.4 in Strogatz.
10. Pointwise and Correlation Dimensions. Section 11.5 in Strogatz.
11. Henon Map. Section 12.2 in Strogatz.
12. Rossler System. Section 12.3 in Strogatz.
13. Forced Double-Well Oscillator. Section 12.5 in Strogatz.
14. Using Chaos to Send Secret Messages. Section 9.6 in Strogtaz.