Ergodic Theory and Fractal Geometry by Hillel Furstenberg - 9781470410346

Ergodic Theory and Fractal GeometryAuthor(s): Hillel Furstenberg\nFormat: Paperback\nPublisher: American Mathematical Society, United States\nImprint: American Mathematical Society\nISBN-13: 9781470410346, 978-1470410346\nSynopsis\nFractal 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. \n\nThe 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 t.