Chaos: the Science of Predictable Motion

This is the title of a book by Richard Kautz. A former Nist colleague, this is a nice account of chaos, in an informal style, but still enough technical details. The most interesting part is the account of Josephson effect and voltage standard development, in which chaos plays an important role in understanding the measurement uncertainty, and in the design of voltage standard, because the mechanism is similar to a pendulum (its chaotic attractor is shown in the picture above).  Kudos to the author for writing an entertaining book.

My own involement with chaos started with my thesis work on chaotic time series. I think one of the famous pictures I developed was the study of predictability of the 3-var Lorenz system (see the picture above, published figure in black and white in Ref 2). I had a few chances to see and talk to E. N. Lorenz while at NCAR. In particular, Lorenz himself continued his work on developing on "toy" examples of simple chaotic models for important experimental and theoretical studies, one of which is the 40-var model he developed around 1996. This model was used in targeted observations study by him and immediately by myself when Berliner and I proposed a Bayesian statistical design framework for the targeted observations problem, On the broader scale, I think chaos theory is nice, in that it connects random and statistical theory to dynamical systems, which are the typical models for physics and sciences. Examples are odes, and mapping in the discrete-time case. After 30 years or so developments of chaos theory in many areas, mostly in mathematics and physics, I think the most promising future developments may lie in the application of chaos theory to emerging areas such as biology or nanotechnology.
References: 1. Richard Kautz, Chaos: The Science of Predictable Random Motion, Oxford University Press, 2011. 2. Zhan-Qian Lu, R.L. Smith, Estimating Local Lyapunov Exponents. In pp.135-150, Nonlinear Dynamics and Time Series. Building a Bridge Between the Natural and Statistical Sciences. Eds Colleen D. Cutler and Daniel T. Kaplan, American Mathematical Society, 1997.