Week 1
He who asks is a fool for five minutes, but he who does not ask remains a fool forever.
Chinese proverb
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Course goals,
as recorded by Professor Zweistein on Halloween (graduates of certain institutions are given to over-dramatizing their own suffering) |
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Welcome to the course |
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Welcome our volunteers |
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About homework |
- 1. Trajectories
- 2. Flow visualized as an iterated mapping
- Homework 1
- Optional
We start out by a recapitulation of the basic notions of dynamics. Our aim is narrow; keep the exposition focused on prerequisites to the applications to be developed here. We assume that you are familiar with nonlinear dynamics on the level of an introductory texts such as Strogatz, and concentrate here on developing intuition about what a dynamical system can do.
Discrete time dynamical systems arise naturally by either strobing the flow at fixed time intervals (we will not do that here), or recording the coordinates of the flow when a special event happens (the Poincaré section method, key insight for much that is to follow).
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Equilibria of the Rössler system, Runge-Kutta integration, and Poincaré sections |
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A gallery of Poincaré sections for Rössler flow |
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Discussion forum for week 1 |
All you need to know about chaos is contained in the introduction
of [ChaosBook]. However, in order to understand
the introduction you will first have to read the rest of the
book.
Gary Morriss
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Chapter 1 - Overture |
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Chapter 1 overheads |
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Appendix A - A brief history of chaos |
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Life in extreme dimensions: What do these equations do? |
We are grateful to Cleo Magnuson for assistance with the design of the course, to Ray Chang for the design of the above B&W icons, and to Edith Greenwood (all of Georgia Tech Professional Education) for shooting the PowerPoint style videos on this page.