I'm looking for some good books on fractals, with a spin to applications in physics. Specifically, applications of fractal geometry to differential equations and dynamical systems, but with emphasis on the physics, even at the expense of mathematical rigor. Hope that was clear and specific enough.
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Uriel Frisch, Turbulence: the legacy of A.N. Kolmogorov. Cambridge University Press, 1995. 296pp.
T. Tél and M. Gruiz, Chaotic Dynamics - An Introduction Based on Classical Mechanics. Cambridge University Press, 2006. 412pp.
Edward Ott, Chaos in Dynamical Systems. Cambridge University Press, 1993. A lot of stuff on chaos, but has a good chapter on measuring fractal dimensions in those systems. The language is straightforward.
Benoit Mandelbrot, The Fractal Geometry of Nature. Henry Holt and Company, 1983, and all of Mandelbrot's books and articles, they are very lucid and full of interesting original ideas. They are also very different from the usual math papers, they are more like physics papers.
There is a wonderful small book by Cardy on renormalization theory [Scaling and Renormalization in Statistical Physics, Cambridge University Press, 1996], and Cardy's papers are classics all, but the papers are not introductory. There is a small issue with condensed matter treatments of this: the field theory intuition is often not as fluent and intuitive as in the high energy treatments, but this is compensated to a degree by the more interesting diverse examples and the explicit calculations.
There are also a string of books from the 1980s, an encyclopedic collection by Domb and Green, and a nice little book by Parisi called "statistical field theory" doing the perturbation theory while trying to sidestep explicit epsilon expansion (although I am not sure the result is so great).
I think the 1974 Reviews of Modern Physics article by Wilson is readable, but in my memory it requires familiarity with path integrals. Perhaps Kadanoff's papers will work, but they assume you know OPE. not sure.
Credit: Piotr Migdal, user9886, GuySoft, Ron Maimon; from deleted answers and comments.
protected by Qmechanic♦ Aug 14 '14 at 20:05
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