
Preface  Preview Material  Table of Contents  Supplementary Material 
CBMS Regional Conference Series in Mathematics 2014; 69 pp; softcover Number: 120 ISBN10: 1470410346 ISBN13: 9781470410346 List Price: US$32 Member Price: US$25.60 Order Code: CBMS/120 See also: Ergodic Theory, Groups, and Geometry  Robert J Zimmer and Dave Witte Morris Invitation to Ergodic Theory  C E Silva Lectures on Fractal Geometry and Dynamical Systems  Yakov Pesin and Vaughn Climenhaga  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 selfsimilarity, 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 selfsimilarity are interpreted in terms of ergodic averages and periodicity of classical dynamics; moreover, the methods have deep implications in combinatorics. The exposition is wellstructured and clearly written, suitable for graduate students as well as for young researchers with basic familiarity in analysis and probability theory. Endre Szemerédi, Rényi Institute of Mathematics, Budapest Fractal geometry represents a radical departure from classical geometry, which focuses on smooth objects that "straighten out" under magnification. Fractals, which take their name from the shape of fractured objects, can be characterized as retaining their lack of smoothness under magnification. The properties of fractals come to light under repeated magnification, which we refer to informally as "zooming in". This zoomingin process has its parallels in dynamics, and the varying "scenery" corresponds to the evolution of dynamical variables. The present monograph focuses on applications of one branch of dynamicsergodic theoryto the geometry of fractals. Much attention is given to the allimportant notion of fractal dimension, which is shown to be intimately related to the study of ergodic averages. It has been long known that dynamical systems serve as a rich source of fractal examples. The primary goal in this monograph is to demonstrate how the minute structure of fractals is unfolded when seen in the light of related dynamics. A copublication of the AMS and CBMS. Readership Graduate students and research mathematicians interested in fractal geometry and ergodic theory. 


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