{"id":"W2015758677","doi":"10.1103/physreve.77.046205","title":"Transcritical bifurcations in nonintegrable Hamiltonian systems","year":2008,"lang":"en","type":"article","venue":"Physical Review E","topic":"Quantum chaos and dynamical systems","field":"Physics and Astronomy","cited_by":11,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Saskatchewan","funders":"","keywords":"Semiclassical physics; Pitchfork bifurcation; Symplectic geometry; Hamiltonian (control theory); Hamiltonian system; Periodic orbits; Mathematics; Bifurcation; Transcritical bifurcation; Quantum; Homogeneous space; Classical mechanics; Mathematical physics; Mathematical analysis; Physics; Bifurcation theory; Quantum mechanics; Geometry; Nonlinear system","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000239041,0.0002002403,0.0003365919,0.0005803317,0.0006067163,0.0006209252,0.0003164381,0.0003571742,0.002036885],"category_scores_gemma":[0.001492186,0.0001557406,0.0002299606,0.0002813495,0.001397318,0.0009349305,0.0006530866,0.0004090861,0.0001001488],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004623713,"about_ca_system_score_gemma":0.0001859445,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007101647,"about_ca_topic_score_gemma":0.0005469071,"domain_scores_codex":[0.9998989,0.00001859754,0.000006062168,0.00001429197,0.00004515139,0.00001689421],"domain_scores_gemma":[0.9997228,0.000113857,0.0000698774,0.00003777098,0.00002570825,0.00003002487],"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":[0.0001064389,0.00009977703,0.007880811,0.0001505932,0.0000425003,0.00146063,0.001683107,0.3272302,0.07517648,0.5682312,0.0004737705,0.01746446],"study_design_scores_gemma":[0.00003107023,0.0000583517,0.003901337,0.00001784036,0.000009715253,0.0003323374,0.0002771124,0.7661123,0.007103661,0.221073,0.001062982,0.00002023204],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9563655,0.0002114269,0.03686486,0.0000902009,0.00001526565,0.00002046194,0.00001538167,0.00007739079,0.006339472],"genre_scores_gemma":[0.9953976,0.00007482013,0.00398918,0.00000733609,0.000005885401,0.000008018202,0.00001334631,0.000009890174,0.0004938793],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002036885,"threshold_uncertainty_score":0.006814122,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02085177902455023,"score_gpt":0.2939568379864164,"score_spread":0.2731050589618662,"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."}}