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Chaos, Dynamics, and Fractals by Joseph L. McCauley

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Introduction

Since the beginning of physics, the study of theoretical mechanics has been synonymous with the study of the gross regularities of nature. Regularity of occurrence either in space or in time depends implicitly upon an underlying stability in the development of chains of events whereby small changes in starting conditions do not produce the need for a statistical description: nearby starting conditions must yield patterns of trajectories that are similar in appearance at later times. At the other extreme lie phenomena where attempts at reproducibility fail. They fail in the sense that ‘repeated identical experiments’, experiments where the starting conditions are as close to one another as experimental error will permit, yield very ...

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