Montreal ASI: SMS july 2007 4 lectures on the N-body problem
Bibliographic record
Abstract
In the first two lectures, hamiltonian techniques are applied to avatars of the N-body problem of interest to astronomers: the first one intro-duces one of the simplest non integrable equations, the planar circular restricted problem in the lunar case, where most degeneracies of the gen-eral (non restricted) problem are not present; the second one is a quick introduction to Arnold’s theorem on the stability of the planetary prob-lem where degeneracies are dealt with thanks to Herman’s normal form theorem. The last two lectures address the general (non perturbative) N-body problem: in the third one, a sketch of proof is given of Marchal’s theorem on the absence of collisions in paths of N-body configurations with given endpoints which are local action minimizers; in the last one, this theorem is used to prove the existence of various families of periodic and quasi-periodic solutions with prescribed symmetries and in particular to extend globally Liapunov families bifurcating from polygonal relative equilibria. Celestial mechanics is famous for demanding extensive compu-tations which hardly appear here: these notes only describe the skeleton on which these computations live.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.003 | 0.001 |
| Scholarly communication | 0.004 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.513 | 0.155 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; the direct Gemma label and the distilled Codex classifier agree on what is shown here.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".