Ergodic Theory and Fractal Geometry (Regional Conference Series in Mathematics, #120) By Hillel Furstenberg Paperback 1470410346 9781470410346 Ergodic Theory and Fractal Geometry (Regional Conference Series in Mathematics, #120) 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 zooming in 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 dynamics ergodic theory to the geometry of fractals. Much attention is given to the all important 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.

Ergodic Theory and Fractal Geometry kindle book

This book was attractive to me because I ve always been fascinated by fractals and if you ve seen some of the amazing illustrations created by Benoit Mandelbrot and his acolytes you ll know why but over one of my favorite professors as an undergraduate Stephen Kalikow was a specialist in ergodic theory So it seemed like an ideal marriage of two interesting disciplines in mathematics and it had the virtue of being fairly brief as well 70 pages This monograph is readable for anyone who has had a first year graduate level education in real analysis In fact reading this book was like a trip down memory lane as Dr Furstenberg pulls out result after result from my graduate real analysis course using Royden s Real Analysis as the guide Fatou s Lemma the Dominating Convergence Theorem the Radon Nikodym Theorem and so on I especially recommend this monograph to anyone who really yearns to learn what the notion of dimension means Paperback

Ergodic Theory and Fractal Geometry (Regional Conference Series in Mathematics, #120) By Hillel Furstenberg

1470410346

9781470410346

English

69

Paperback

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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 zooming in 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 dynamics ergodic theory to the geometry of fractals Much attention is given to the all important 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 Ergodic Theory and Fractal Geometry Regional Conference Series in Mathematics 120 .