For those of you who would like to read more about the basics of applied ergodic theory that I talked about in 703 today, there are a few accessible papers and books below the fold. You are always very welcome to send me an e-mail or drop by my office (VV517) if you want to talk more about any of the papers or the topic in general.
Please e-mail me if any of the links below the fold don’t work, or if you have trouble locating the pdfs for the papers.
Here’s a simple demonstration of Arnold’s Cat Map. V.I. Arnold, a cool cat himself, figured out, decades before the age of the internet, that putting an image of a kitteh in your research vastly increases its appeal.
- The perspective and approach of ergodic theory.
Petersen, K. (1996). Ergodic theorems and the basis of science. Synthese. An International Journal for Epistemology, Methodology and Philosophy of Science, 108(2), 171–183. doi:10.1007/BF00413496
- A good overview of how ergodic theory interacts with dynamical systems. One of the most widely read intro papers in the field.
Eckmann, J., & Ruelle, D. (1985). Ergodic theory of chaos and strange attractors. Reviews of modern physics, 57(3), 617–656. doi:10.1103/RevModPhys.57.617
- We didn’t get to talk about this, but entropy is another of those basic topics in ergodic theory. This is a particularly approachable introduction. L-S Young has other good expository papers that she shares on her website.
Young, L.-S. (2003). Entropy in Dynamical Systems. In Entropy. [pdf]
- A review I co-authored. The whole paper is long, but introduction conveys what I talked about in terms of “approach and perspective”
Budišić, M., Mohr, R., & Mezić, I. (2012). Applied Koopmanism. Chaos: An Interdisciplinary Journal of Nonlinear Science, 22(4), 047510–1–33. doi:10.1063/1.4772195
- A very approachable text to “applied” ergodic theory and stochastic dynamics
Lasota, A., & Mackey, M. C. (1995). Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics, 2nd Ed. Berlin: Springer-Verlag. [Math library]
- A “gentle” introduction to ergodic theory, including a review of real analysis.
Silva, C. E. (2008). Invitation to ergodic theory (Vol. 42). Providence, RI: American Mathematical Society. [Math library]