The sand grain and the butterfly. Instability in geodesy and geophysics
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Abstract
The problems of convergence of series in celestial mechanics and of certain series in geodesy (Molodensky's series and spherical harmonics) show similar features, involving a curious instability. This is imaginatively expressed as the « butterfly effect» in chaos theory and the «sand-grain effect» for spherical harmonics. Similarly, the geodetic boundary-value problem (M.S. Molodensky, L. Hormander) and the KAM problem in nonlinear dynamics have a common mathematical structure: a «hard» inverse function problem. Such interrelations are reviewed in the present paper.
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Moritz H. The sand grain and the butterfly. Instability in geodesy and geophysics. Ann. Geophys. [Internet]. 1997Nov.25 [cited 2021Oct.22];40(5). Available from: https://www.annalsofgeophysics.eu/index.php/annals/article/view/3871
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