Math 7170 / TAM 7760 Applied Dynamical Systems
Fall 2009
Prof. Steven Strogatz, 212 Kimball Hall, 5-5999, strogatz@cornell.edu
Office hours: Monday 2-4
Texts (required)
1. “GH” = Guckenheimer and Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields|
Core ideas of dynamical systems theory (Chap.1, GH) |
~2 weeks |
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Duffing oscillator with negative stiffness (2.2, GH) |
~1 week |
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Melnikov’s method (4.5, GH) |
~2 weeks |
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Horseshoes, symbolic dynamics, homoclinic tangles (5.0-5.3, GH) |
~2 weeks |
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Center manifold theory (3.2 in GH, and Chap. 5 in K) |
~2 weeks |
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One-parameter bifurcations (Chaps. 3 and 7, K, and 3.3, GH) |
~2 weeks |
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Two-parameter bifurcations (7.1-7.3, GH and 8.1-8.5, K) |
~2 weeks |
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Bifurcations with symmetry (7.4, K) |
if time permits |
Grading Take-home final exam (assigned one week before the end of classes, and due at the last lecture). 5 or 6 problem sets (assigned roughly every two weeks. These are for practice, but I’m not sure yet if they’ll be graded. Solutions will be made available.)
Prerequisites
TAM 5780 or equivalent background in nonlinear dynamics. (TAM 5780 covers phase plane, bifurcations of fixed points and limit cycles, Lorenz equations, logistic map, period doubling, and fractals.) Math 6170 and TAM 6750 will be helpful but are not required. StyleThis course will be intuitive, geometric, careful, and concrete, but not proof-oriented or mathematically rigorous. There will be a few scientific applications, but not nearly as many as in TAM 5780.
Homework
You can download homework 3 here. It's due October 27.
Here is homework 4, due Tuesday, November 10.