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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Week 1 overview |
- 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.
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Chapter 2 - Go with the flow Each chapter pdf file has hyperlinks to all videos listed below. The intention is that you study the chapter, and click on video links whenever you would like to see the text explained in a live lecture. In other words, ChaosBook is the primary mode of study, videos play only a supporting role. Let us know in a Piazza forum how this works for you. |
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Chapter 2 overheads |
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Dynamical systems If you are falling asleep watching a lecturer scribble on a tablet in a dark room while reading aloud from PowerPoint slides on a teleprompter, please hang in there. Professional Educators told us that is how Distance Education works. We tried it and are not convinced, so by week 2 we will revert to live blackboard lectures, with screeching chalk and students bugging the lecturer in real time. |
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Trajectories |
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Lorenz flow |
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Equilibria |
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Strange attractors |
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Strange attractors - Lorenz again |
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Strange repellers - a game of pinball |
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Lorenz again (apologies) |
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Roessler flow |
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Computing is like hygiene, personal |
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Dynamical systems : a summary |
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Orbits are time-invariant |
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Life in extreme dimensions: Fluttering flame front |
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Life in extreme dimensions: Constructing state spaces |
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Life in extreme dimensions: As visualized by dummies |
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Life in extreme dimensions:
Go where the action is 27 January 2015: still to be recorded |
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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Chapter 3 - Discrete time dynamics |
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Chapter 3 overheads |
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Life in extreme dimensions: Poincaré sections |
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Poincaré sections for Rössler flow |
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Poincaré sections |
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Mappings |
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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.