The sand grain and the butterfly. Instability in geodesy and geophysics

Main Article Content

H. Moritz

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.

Article Details

How to Cite
1.
Moritz H. The sand grain and the butterfly. Instability in geodesy and geophysics. Ann. Geophys. [Internet]. 1997Nov.25 [cited 2021Jun.24];40(5). Available from: https://www.annalsofgeophysics.eu/index.php/annals/article/view/3871
Section
OLD