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Ergodic Theory and Fractal Geometry

Hillel Furstenberg
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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.
      Format: Paperback / softback CONTRIBUTORS: Hillel Furstenberg EAN: 9781470410346 COUNTRY: United States PAGES: WEIGHT: 158 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2014-08-30 CITY: GENRE: MATHEMATICS / Differential Equations / General, MATHEMATICS / Geometry / General, MATHEMATICS / Topology WIDTH: 178 cm SPINE:

      Book Themes:

      Differential calculus and equations, Geometry, Topology

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      Hillel Furstenberg, The Hebrew University of Jerusalem, Israel
      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.
      Format: Paperback / softback CONTRIBUTORS: Hillel Furstenberg EAN: 9781470410346 COUNTRY: United States PAGES: WEIGHT: 158 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2014-08-30 CITY: GENRE: MATHEMATICS / Differential Equations / General, MATHEMATICS / Geometry / General, MATHEMATICS / Topology WIDTH: 178 cm SPINE:

      Book Themes:

      Differential calculus and equations, Geometry, Topology

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      Hillel Furstenberg, The Hebrew University of Jerusalem, Israel

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