Ergodic Theory and Fractal Geometry (Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, 120, Band 120) - Softcover

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In notes for a lecture series he delivered, Furstenberg shows that ergodic theoretical concepts can be applied to the process of changing magnification to give insight into phenomena peculiar to fractals. An important step, he says, is showing how fractal dimension can be interpreted in terms of ergodic averages in an appropriate measure-preserving system. The familiar phenomenon of self-similarity appears as the analogue of periodicity in classical dynamics. He does not pursue the full implications of recurrence in the geometric context, but considers some examples of the related Ramsey type questions. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

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