Invariant tori for multi-dimensional integrable Hamiltonians coupled to a single thermostat
Bibliographic record
Abstract
Abstract This paper demonstrates sufficient conditions for the existence of Kolmogorov-Arnol’d-Moser (KAM) tori in a singly thermostated, integrable Hamiltonian system with n degrees of freedom with a focus on the generalized, variable-mass thermostats of order 2—which include the Nosé thermostat, the logistic thermostat of Tapias, Bravetti and Sanders, and the Winkler thermostat. It extends theorem 3.2 of Legoll et al (2009 Nonlinearity 22 1673–94) to prove that a ‘typical’ singly thermostated, integrable, real-analytic Hamiltonian possesses a positive-measure set of invariant tori when the thermostat is weakly coupled. It also demonstrates a class of integrable Hamiltonians, which, for a full-measure set of couplings, satisfies the same conclusion.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
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".