The sand grain and the butterfly. Instability in geodesy and geophysics
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 effe...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Istituto Nazionale di Geofisica e Vulcanologia (INGV)
1997-06-01
|
| Series: | Annals of Geophysics |
| Subjects: | |
| Online Access: | http://www.annalsofgeophysics.eu/index.php/annals/article/view/3871 |
| _version_ | 1818241804353404928 |
|---|---|
| author | H. Moritz |
| author_facet | H. Moritz |
| author_sort | H. Moritz |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-12T13:35:09Z |
| format | Article |
| id | doaj.art-e7eebe2fcf3f44239d064dee07503c5c |
| institution | Directory Open Access Journal |
| issn | 1593-5213 2037-416X |
| language | English |
| last_indexed | 2024-12-12T13:35:09Z |
| publishDate | 1997-06-01 |
| publisher | Istituto Nazionale di Geofisica e Vulcanologia (INGV) |
| record_format | Article |
| series | Annals of Geophysics |
| spelling | doaj.art-e7eebe2fcf3f44239d064dee07503c5c2022-12-22T00:22:59ZengIstituto Nazionale di Geofisica e Vulcanologia (INGV)Annals of Geophysics1593-52132037-416X1997-06-0140510.4401/ag-3871The sand grain and the butterfly. Instability in geodesy and geophysicsH. MoritzThe 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.http://www.annalsofgeophysics.eu/index.php/annals/article/view/3871Geodesygeophysicsgravity fieldinstabilitychaos theory |
| spellingShingle | H. Moritz The sand grain and the butterfly. Instability in geodesy and geophysics Annals of Geophysics Geodesy geophysics gravity field instability chaos theory |
| title | The sand grain and the butterfly. Instability in geodesy and geophysics |
| title_full | The sand grain and the butterfly. Instability in geodesy and geophysics |
| title_fullStr | The sand grain and the butterfly. Instability in geodesy and geophysics |
| title_full_unstemmed | The sand grain and the butterfly. Instability in geodesy and geophysics |
| title_short | The sand grain and the butterfly. Instability in geodesy and geophysics |
| title_sort | sand grain and the butterfly instability in geodesy and geophysics |
| topic | Geodesy geophysics gravity field instability chaos theory |
| url | http://www.annalsofgeophysics.eu/index.php/annals/article/view/3871 |
| work_keys_str_mv | AT hmoritz thesandgrainandthebutterflyinstabilityingeodesyandgeophysics AT hmoritz sandgrainandthebutterflyinstabilityingeodesyandgeophysics |