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Ergodic Theory and Fractal Geometry

Harry Furstenberg

出版	Conference Board of the Mathematical Sciences, 2014
ISBN	14704185419781470418540
URL	http://books.google.com.hk/books?id=VXW9swEACAAJ&hl=&source=gbs_api

註釋

Fractals are beautiful and complex geometric objects. Their study, pioneered by Benoît Mandelbrot, is of interest in mathematics, physics and computer science. Their inherent structure, based on their self-similarity, makes the study of their geometry amenable to dynamical approaches. In this book, a theory along these lines is developed by Hillel Furstenberg, one of the foremost experts in ergodic theory, leading to deep results connecting fractal geometry, multiple recurrence, and Ramsey theory. In particular, the notions of fractal dimension and self-similarity are interpreted in terms of e.