Indeholder "Foreword", "Introduction", "Part I. Steps to a deterministic interpretation of chaotic signals", " 1. Descriptions of turbulence", " 2. A bit more on turbulence. The Navier–Stokes equation", " 3. The Hénon mapping", " 4. Capacity and Hausdorff dimension", " 5. Attracting sets and attractors", " 6. Extracting geometric information from a times series", "Part II. The ergodic theory of chaos", " 7. Invariant probability measures", " 8. Physical measures", " 9. Characteristic exponents", " 9.1 The multiplicative ergodic theorem", " 9.2 Characteristic exponents in localisation theory", " 9.3 Characteristic exponents in differentiable dynamics ", " 9.4 The spectrum of characteristic exponents as a classification tool", " 9.5 Parameter dependence", " 9.6 Experimental determination of characteristic exponents", " 10. Invariant manifolds", " 11. Axiom A and structural stability", " 12. Entropy", " 12.1 Entropy and characteristic exponents", " 12.2 SRB measures", " 13. Dimensions", " 13.1 Strange attractors as inhomogeneous fractals", " 13.2 Information dimension, entropy and characteristic exponents", " 14. Resonances", " 15. Conclusions", "References", "Bibliography", "Index".

Lidt om kaosteori og strange attractors. ( )

I checked this book out from the library when we were talking about chaos theory in a business class (required for my degree). I wanted a little bit of the mathematical background as a sanity check, but seeing as the topic was going to be covered in about two hours, I couldn't see committing to months preparing the math. I was happy with how that turned out and think this book was a good choice for that job. It's a short book (around 90 pages, depending on how you count), and is mainly explication rather than proof, a tour treated more casually than would be in a class. While I wouldn't recommend the book as a primary text for study, I can see it serving as an introduction or supplement to more rigorous treatment (another textbook or reading the original papers).

Prereq's: my BA in mathematics served me in good stead. I knew most of the terminology and concepts and was able to mostly follow what was going on, could probably have picked up a few more minor points if I'd gone to Wikipedia for definitions. I would not recommend trying to read this without some undergraduate analysis and topology. The one thing I thought was that I could stand to learn something like differential geometry, and obviously, the more background you have the more you will understand.

Topics covered:
definition and geometry of chaos
relevant kinds of dimensions, probabilities, and other measures
definition and kinds of attractors
characteristic exponents
entropy and information ( )