Ergodic Theory and Fractal Geometry

Furstenberg, Hillel

ISBN 10: 1470410346 / ISBN 13: 9781470410346

Published by American Mathematical Society, 2014

Unread book in perfect condition. Seller Inventory # 21600142

Synopsis:

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.

About the Author: Hillel Furstenberg, The Hebrew University of Jerusalem, Israel

Bibliographic Details

Title: Ergodic Theory and Fractal Geometry
Publisher: American Mathematical Society
Publication Date: 2014
Binding: Soft cover
Condition: As New