{"id":"W2049229557","doi":"10.3934/dcds.2006.14.845","title":"Unique ergodicity, stable ergodicity, and the Mautner phenomenon for diffeomorphisms","year":2006,"lang":"en","type":"article","venue":"Discrete and Continuous Dynamical Systems","topic":"Geometry and complex manifolds","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Ergodicity; Mathematics; Geodesic; Pure mathematics; Context (archaeology); Manifold (fluid mechanics); Simple (philosophy); Flow (mathematics); Dynamical systems theory; Constant (computer programming); Curvature; Mathematical analysis; Physics; Geometry; Quantum mechanics; Computer science","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0007409188,0.0002999686,0.000702738,0.00006098497,0.0003552077,0.0002789977,0.0002315446,0.0001561666,0.00001349669],"category_scores_gemma":[0.00006936961,0.0001892881,0.0001229343,0.0001350955,0.000332208,0.00009371464,0.0001718222,0.0001760994,0.000001773321],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003373962,"about_ca_system_score_gemma":0.00001282085,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001485198,"about_ca_topic_score_gemma":0.0002580873,"domain_scores_codex":[0.9981591,0.0001788478,0.0005269353,0.0004027872,0.0002616509,0.0004707313],"domain_scores_gemma":[0.9984953,0.0007773331,0.0001947387,0.0003418274,0.00008181463,0.0001089297],"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":[0.0002190997,0.00008739062,0.001662278,0.0003192941,0.00008241541,0.000006146807,0.0001485286,0.00002407462,0.000467663,0.9954039,0.00126584,0.0003132945],"study_design_scores_gemma":[0.009533624,0.0005357529,0.004840774,0.0003065914,0.000527201,0.0001942233,0.001685997,0.1423848,0.00008852111,0.8260193,0.01273568,0.001147512],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8942084,0.001235666,0.09323139,0.0008984564,0.0002285229,0.001892029,0.0001285912,0.000155556,0.008021424],"genre_scores_gemma":[0.9928126,0.00002415024,0.0003240575,0.00007662893,0.000219212,0.0002389718,0.00003981882,0.00003900854,0.006225504],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1693847,"threshold_uncertainty_score":0.7718945,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01321806051421101,"score_gpt":0.2424678260850178,"score_spread":0.2292497655708068,"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."}}