{"id":"W1954234108","doi":"10.1016/j.matpur.2015.09.006","title":"Action-angle variables and a KAM theorem for b-Poisson manifolds","year":2015,"lang":"fr","type":"article","venue":"Journal de Mathématiques Pures et Appliquées","topic":"Homotopy and Cohomology in Algebraic Topology","field":"Mathematics","cited_by":24,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"Agència de Gestió d'Ajuts Universitaris i de Recerca; Ministerio de Economía y Competitividad; European Science Foundation","keywords":"Uniqueness theorem for Poisson's equation; Kolmogorov–Arnold–Moser theorem; Mean value theorem (divided differences); Poisson distribution; Manifold (fluid mechanics); Danskin's theorem; Carlson's theorem; Representation theorem","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.003933157,0.0004903056,0.0007981223,0.0002055591,0.0003520272,0.000412578,0.0004302747,0.0008881285,0.0003398996],"category_scores_gemma":[0.001070887,0.0004434366,0.0002350219,0.0001358132,0.0004222841,0.0004523096,0.000172912,0.0009641026,0.00004308521],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002947245,"about_ca_system_score_gemma":0.0005937871,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008489802,"about_ca_topic_score_gemma":0.0001917919,"domain_scores_codex":[0.9967739,0.0008161275,0.0008659145,0.0003796941,0.0003188005,0.0008455682],"domain_scores_gemma":[0.9964386,0.00165687,0.0006521495,0.0003612341,0.0003543182,0.0005368841],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00026823,0.0003704033,0.0002167375,0.0006383362,0.0003571174,0.0001458708,0.008648752,0.00001985143,0.0003638281,0.8848016,0.09819931,0.005969952],"study_design_scores_gemma":[0.001130757,0.0007479278,0.0001131595,0.0002722007,0.0003542573,0.008087984,0.002555266,0.0009082898,0.001836254,0.8467874,0.1368202,0.0003863277],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5307865,0.03242477,0.3321587,0.0683817,0.004132784,0.002310978,0.0001915417,0.0004320468,0.02918098],"genre_scores_gemma":[0.5556594,0.0116372,0.3866649,0.005416496,0.004724674,0.0007018753,0.00003404002,0.0003773292,0.03478409],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.06296521,"threshold_uncertainty_score":0.9998018,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04925453632280558,"score_gpt":0.3480157152032634,"score_spread":0.2987611788804578,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}