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  Fractals in physics. Suggest book titles

+ 5 like - 0 dislike

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. Thanks.

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asked May 4, 2014 in Resources and References by PKM2 (0 points) [ revision history ]
retagged May 4, 2014 by dimension10

All of renormalization physics is "fractals", in a sense, so this is the entire field of phase transitions, anomalous dimensions, and operator products. It's very big.

I like "The Fractal Geometry of Nature", 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, and Cardy's papers are classics all, but the papers are not introductory. 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.

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@RonMaimon Do you mean this book: Scaling and renormalization in statistical physics by John Cardy?. I have it. Do you recommend it? Maybe I'll read it.

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Yes, that's the one. 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).

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I've heard positive things about "Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering" by Steven H. Strog but haven't really read it myself.

2 Answers

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  • Uriel Frisch, Turbulence: the legacy of A.N. Kolmogorov, Cambridge University Press, 1995 - Science - 296 pages

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answered May 4, 2014 by Piotr Migdal (1,260 points) [ no revision ]
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This book contains a short but well written chapter on fractals (with a focus on the dimension-spectrum):

T. Tél and M. Gruiz, Chaotic Dynamics -- An Introduction Based on Classical Mechanics (Cambridge University Press, 2006), p. 412.

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answered May 4, 2014 by user9886 (85 points) [ no revision ]

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