{"id":"W2071479141","doi":"10.1142/s0218127407018208","title":"ON THE NUMBER OF LIMIT CYCLES IN NEAR-HAMILTONIAN POLYNOMIAL SYSTEMS","year":2007,"lang":"en","type":"article","venue":"International Journal of Bifurcation and Chaos","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":26,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"","keywords":"Hamiltonian system; Mathematics; Periodic orbits; Limit cycle; Hamiltonian (control theory); Center (category theory); Polynomial; Limit (mathematics); Mathematical analysis; Pure mathematics; Discrete mathematics; Mathematical optimization","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":[],"consensus_categories":[],"category_scores_codex":[0.00053741,0.00006791216,0.0001441123,0.00009957149,0.00003034674,0.00003936775,0.0001602959,0.00004616995,0.00003536653],"category_scores_gemma":[0.0002791414,0.00004446231,0.00005524997,0.00007387005,0.00004855521,0.0000808678,0.00001825211,0.000118199,0.000004180572],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006302447,"about_ca_system_score_gemma":0.00002968065,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00006175335,"about_ca_topic_score_gemma":0.00004341735,"domain_scores_codex":[0.9988904,0.00004397779,0.0005704593,0.00006184763,0.0003557786,0.00007750987],"domain_scores_gemma":[0.9986272,0.0005648424,0.0004567423,0.00007450351,0.0002368407,0.000039897],"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":[0.0004563782,0.0005575794,0.01874751,0.00004433534,0.0001659767,0.00001741525,0.001949198,0.0005186743,0.002349323,0.9593353,0.0004103598,0.01544793],"study_design_scores_gemma":[0.01309098,0.0008687865,0.4215738,0.004049211,0.0001905353,0.001237516,0.01276197,0.06901176,0.005773469,0.4573004,0.01286921,0.001272299],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9768864,0.00004288758,0.02041623,0.0008064691,0.0005258776,0.00009690694,0.000005749974,0.000003920933,0.001215595],"genre_scores_gemma":[0.9991325,0.00002078269,0.0004980411,0.00005377037,0.0001691928,0.000001988944,0.000001446046,0.000006648614,0.0001155977],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5020349,"threshold_uncertainty_score":0.181312,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03037395234865919,"score_gpt":0.3460151514081207,"score_spread":0.3156411990594615,"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."}}