Week 3
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Week 3 overview |
- 5. Stability exponents are invariants of dynamics
- Homework 3
We prove that (i) Floquet multipliers are the same everywhere along a cycle, and (ii) that they are invariant under any smooth coordinate transformation.
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Periodic orbit of the Rössler system |
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Chapter 7 - Fixed points |
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Homework 3 walkthrough |
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Discussion forum for week 3 |
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Summary of the course, so far |
In the world of everyday, moderately turbulent fluids flowing across planes and down pipes, a velvet revolution is taking place. Experiments are as detailed as simulations, there is a zoo of exact numerical solutions that one dared not dream about a decade ago, and portraits of turbulent fluid's state space geometry are unexpectedly elegant. We take you on a tour of this newly breached, hitherto inaccessible territory. Mastery of fluid mechanics is no prerequisite, and perhaps a hindrance: the tutorial is aimed at anyone who had ever wondered how we know a cloud when we see one, if no cloud is ever seen twice? And how do we turn that into mathematics?
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Tutorial - A stroll through 61,506 dimensions Ladies and gentlemen, this is no model: this is Navier-Stokes! |
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Delirious ambitions |
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What have we learned? |
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Quantum chaos |
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Gutzwiller semiclassical quantization |
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Be brave: do QFT |
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From fluid dynamics to Yang-Mills |
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Knowing where to stop: h-bar |
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Turbulence (optional: earn bonus points) |
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Daniel Kleppner - Quantum Mechanics and Chaos |
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Richard Feynman - The Principle of Least Action |