Tell me more ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.
up vote 3 down vote favorite
2

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.

share|improve this question
1  
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. – Ron Maimon Jun 15 '12 at 17:58
@RonMaimon Can you suggest a few references? Preferably books; papers if they are easy to read and can be used as introductions. – becko Jun 15 '12 at 19:37
1  
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. – Ron Maimon Jun 16 '12 at 6:57
@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. – becko Jun 16 '12 at 15:06
1  
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). – Ron Maimon Jun 16 '12 at 17:10

2 Answers

up vote 2 down vote

E.g.

  • Uriel Frisch, Turbulence: the legacy of A.N. Kolmogorov, Cambridge University Press, 1995 - Science - 296 pages
share|improve this answer
up vote 0 down vote

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.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.