Gibb's overshoot on a fractal

David A. Noever

Physica A: Statistical Mechanics and its Applications, 1993, vol. 199, issue 3, 341-349

Abstract: Gibbs' overshoot refers to the persistent discrepancy between a Fourier series' approximation and actual values near a functional discontinuity. Here this phenomenon is generalized to a fractal discontinuity on a trial function. Analytic results support the conclusion that fractal dimension can parameterize the Gibbs' overshoot on an example sawtooth with a fractal distribution of discontinuous depths. Simulations confirm this finding on a fractal Brownian walk and the devil's staircase. Results indicate that the overshoot arises on a fractal not as much from any general ruggedness, but more from the fractal discontinuity directly.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:199:y:1993:i:3:p:341-349

DOI: 10.1016/0378-4371(92)00211-J

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