Low dimensional completely resonant tori in Hamiltonian Lattices and a Theorem of Poincaré
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Bibliographic record
Abstract
We present an extension of a classical result of Poincaré (1892) about continuation of periodic orbits and breaking of completely resonant tori in a class of nearly integrable Hamiltonian systems, which covers most Hamiltonian Lattice models. The result is based on the fixed point method of the period map and exploits a standard perturbation expansion of the solution with respect to a small parameter. Two different statements are given, about existence and linear stability: a first one, in the so called non-degenerate case, and a second one, in the completely degenerate case. A pair of examples inspired to the existence of localized solutions in the discrete NLS lattice is provided.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it