{"id":"W2980338188","doi":"10.4153/s0008439519000626","title":"Limit Cycles of a Perturbation of a Polynomial Hamiltonian Systems of Degree 4 Symmetric with Respect to the Origin","year":2019,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Quartic function; Hamiltonian system; Hamiltonian (control theory); Perturbation (astronomy); Limit cycle; Degree (music); Limit (mathematics); Mathematical analysis; Mathematical physics; Pure mathematics; Quantum mechanics; Mathematical optimization; Physics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004179595,0.0001691126,0.000585776,0.0003003003,0.00004316294,0.00001924042,0.0003043049,0.0000975371,0.0005628634],"category_scores_gemma":[0.0009512004,0.0001054153,0.0001023406,0.0005128984,0.00008935549,0.00002211625,0.00003052428,0.0001090352,0.0002350981],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000131811,"about_ca_system_score_gemma":0.0001794976,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003253844,"about_ca_topic_score_gemma":0.002623728,"domain_scores_codex":[0.99831,0.0001047157,0.0007095739,0.0002016726,0.0003969737,0.000277014],"domain_scores_gemma":[0.9975879,0.001084477,0.000326967,0.0005549937,0.0002087182,0.0002369902],"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":[0.0001279788,0.0001878785,0.000733041,0.001636759,0.0001369006,0.000003732845,0.001218341,0.000476747,0.0007628956,0.992061,0.001694922,0.0009597806],"study_design_scores_gemma":[0.02227406,0.01511186,0.04067874,0.03365876,0.003379739,0.0005494737,0.0328533,0.1907089,0.01099206,0.5236039,0.1178636,0.008325648],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9523981,0.0001003721,0.03273483,0.0009533074,0.0001081622,0.001640033,0.0001182424,0.00002068973,0.01192622],"genre_scores_gemma":[0.9924711,0.000001458067,0.00567118,0.00002502323,0.00003814369,0.00003981295,0.000003897351,0.00002888098,0.001720482],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4684572,"threshold_uncertainty_score":0.616296,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03799850379427426,"score_gpt":0.2639679789606289,"score_spread":0.2259694751663546,"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."}}