{"id":"W2140959905","doi":"10.1016/j.chaos.2004.09.036","title":"Small limit cycles bifurcating from fine focus points in cubic order Z2-equivariant vector fields","year":2004,"lang":"en","type":"article","venue":"Chaos Solitons & Fractals","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":76,"is_retracted":false,"has_abstract":false,"ca_institutions":"Western University","funders":"","keywords":"Equivariant map; Vector field; Focus (optics); Limit (mathematics); Saddle point; Mathematics; Mathematical analysis; Order (exchange); Limit cycle; Point (geometry); Pure mathematics; Physics; Geometry; Optics","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":[0.0001909413,0.0003108943,0.0005635269,0.0001463073,0.0001378752,0.00007567091,0.0002823331,0.0002372269,0.000239701],"category_scores_gemma":[0.001325413,0.0002739759,0.0001448735,0.0003422634,0.00005522483,0.000175008,0.0001349729,0.0003566309,0.0001178251],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001798897,"about_ca_system_score_gemma":0.0000920153,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00217056,"about_ca_topic_score_gemma":0.003367967,"domain_scores_codex":[0.9979894,0.00008746644,0.0006896327,0.0004540974,0.0002565175,0.0005228465],"domain_scores_gemma":[0.997981,0.0009211567,0.0002747837,0.0005626306,0.00009665503,0.0001637964],"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":[0.0004209203,0.009244862,0.009329134,0.0009110853,0.0008688531,0.0005254048,0.03499345,0.008791407,0.09628838,0.762172,0.0003831538,0.07607137],"study_design_scores_gemma":[0.00219025,0.0001330056,0.004298145,0.0005920239,0.00007455107,0.00001105945,0.0005527269,0.008224742,0.007286729,0.9757996,0.000172407,0.000664793],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8503035,0.0001685004,0.1464475,0.001073963,0.0003028751,0.0004644713,0.00006941731,0.0001322286,0.001037554],"genre_scores_gemma":[0.9800287,0.00001017459,0.01911713,0.00006425343,0.0004097955,0.00009838773,0.00004862998,0.00005502671,0.0001678525],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2136276,"threshold_uncertainty_score":0.9999713,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06168198548214264,"score_gpt":0.3085774373031356,"score_spread":0.2468954518209929,"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."}}