Ergodic Theory and Fractal Geometry - Couverture souple

Furstenberg, Hillel

 
9781470410346: Ergodic Theory and Fractal Geometry
Couverture souple
ISBN 10 : 1470410346 ISBN 13 : 9781470410346
Editeur : American Mathematical Society, 2014

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l'auteur

Hillel Furstenberg, The Hebrew University of Jerusalem, Israel

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2014
Langue
anglais
ISBN 10 
1470410346
ISBN 13 
9781470410346
Reliure
Broché
Nombre de pages
69
Coordonnées du fabricant
non disponible
Personne responsable
non disponible