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.
Keywords
Geodesy;geophysics;gravity field;instability;chaos theory
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DOI: https://doi.org/10.4401/ag-3871
Published by INGV, Istituto Nazionale di Geofisica e Vulcanologia - ISSN: 2037-416X