{"id":"W2760932547","doi":"10.3934/jgm.2017017","title":"Instability criterion for periodic solutions with spatio-temporal symmetries in Hamiltonian systems","year":2017,"lang":"en","type":"article","venue":"The Journal of Geometric Mechanics","topic":"Quantum chaos and dynamical systems","field":"Physics and Astronomy","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"","keywords":"Homogeneous space; Linear subspace; Mathematics; Subspace topology; Equivariant map; Hamiltonian (control theory); Periodic boundary conditions; Boundary value problem; Hamiltonian system; Pure mathematics; Instability; Mathematical physics; Symmetry group; Mathematical analysis; Lagrangian; Physics; Quantum mechanics; Geometry; 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":[0.002260998,0.0001421619,0.0003941554,0.0003264172,0.0005343134,0.0002251287,0.0004971454,0.00004772307,0.00002085195],"category_scores_gemma":[0.0002221439,0.00008373624,0.0001185116,0.0004401006,0.00005750342,0.0002796954,0.00007274712,0.000238648,0.000002706323],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008885175,"about_ca_system_score_gemma":0.0001335258,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001271848,"about_ca_topic_score_gemma":0.0001409213,"domain_scores_codex":[0.9985986,0.0001151203,0.0005654473,0.0001124574,0.0003188572,0.000289461],"domain_scores_gemma":[0.9979245,0.0002575059,0.0009094917,0.0004216224,0.0003889698,0.00009788354],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.003349395,0.002488669,0.4424377,0.001041664,0.001187761,0.0000306755,0.003979208,0.01071642,0.0011798,0.4844018,0.002127596,0.04705926],"study_design_scores_gemma":[0.02073896,0.009508703,0.1537536,0.002279289,0.001168277,0.0002894974,0.02196184,0.6676728,0.0008410311,0.08361093,0.03562604,0.002549084],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7274724,0.0003894689,0.2705615,0.0003873736,0.0005583219,0.0004127347,0.0000562075,0.000004835965,0.0001571113],"genre_scores_gemma":[0.9993771,0.00001564388,0.0002584329,0.000008965204,0.0002510583,0.000009991216,0.000005396764,0.00001374321,0.00005963533],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6569563,"threshold_uncertainty_score":0.4109561,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02886096092321558,"score_gpt":0.2622210747070685,"score_spread":0.2333601137838529,"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."}}