{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001123045,0.0001607189,0.0004904909,0.00002806538,0.00008338984,0.00001668053,0.0001571179,0.00001788623,0.0001105591],"category_scores_gemma":[0.00001276297,0.0001248769,0.0002015814,0.0003110329,0.00007516827,0.00009909354,0.00001505579,0.000217186,0.0003649515],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002820968,"about_ca_system_score_gemma":0.00004824685,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008814673,"about_ca_topic_score_gemma":0.000008895065,"domain_scores_codex":[0.9988137,0.00009265086,0.0003409596,0.0002501426,0.0001940949,0.0003084478],"domain_scores_gemma":[0.9994153,0.000100884,0.0000428571,0.0002516953,0.00004569304,0.0001436028],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.000004115196,0.0009796171,0.01144633,0.0008326578,0.00003352443,0.00001228393,0.0002020984,0.00008697899,0.0007113803,0.9810513,0.001875551,0.002764164],"study_design_scores_gemma":[0.005550516,0.000732259,0.06581613,0.03693428,0.0005241592,0.0001135875,0.0007654155,0.2998702,0.0005595759,0.1047212,0.4794449,0.004967693],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8106517,0.02327731,0.0124602,0.00311788,0.0005861178,0.002357228,0.0001594928,0.0001719674,0.1472182],"genre_scores_gemma":[0.9986108,0.0004364551,0.00003298461,0.000110177,0.0002944946,0.0001763497,0.00002637824,0.00001619679,0.0002961465],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.8763301,"threshold_uncertainty_score":0.5092332,"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."}}