{"id":"W1965888997","doi":"10.4153/cmb-2003-034-4","title":"Characterizing Two-Dimensional Maps Whose Jacobians Have Constant Eigenvalues","year":2003,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Eigenvalues and eigenvectors; Jacobian matrix and determinant; Affine transformation; Constant (computer programming); Polynomial; Pure mathematics; Function (biology); Nonlinear system; Mathematical analysis; Applied mathematics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004352128,0.0004076034,0.0002863286,0.00129155,0.0005881374,0.001518721,0.0003284919,0.0006458686,0.001585815],"category_scores_gemma":[0.002145925,0.0001991793,0.0002181992,0.0005082374,0.001890058,0.001199476,0.0009610155,0.0004501237,0.0001936641],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006678769,"about_ca_system_score_gemma":0.0002807351,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008750578,"about_ca_topic_score_gemma":0.0003972222,"domain_scores_codex":[0.9997676,0.00004122035,0.00001257982,0.00004805246,0.00007339392,0.00005705593],"domain_scores_gemma":[0.9990289,0.0003053936,0.0002607274,0.00008128322,0.0001762378,0.0001474607],"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":[0.0001311763,0.0001009146,0.003651843,0.0000978875,0.00002005219,0.0007443463,0.0009773234,0.03214143,0.04024363,0.903179,0.001365838,0.01734669],"study_design_scores_gemma":[0.00005177179,0.0001071508,0.003235273,0.00002139721,0.00001198955,0.0005391165,0.0006295185,0.2171505,0.01018737,0.7644491,0.00354449,0.00007234021],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8786787,0.0002290849,0.1021542,0.0003027582,0.00004424092,0.00004318131,0.00006973268,0.0001126674,0.01836541],"genre_scores_gemma":[0.9914145,0.00007543426,0.006105108,0.00001790742,0.00001913137,0.00001518774,0.00003322286,0.00001387388,0.002305566],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.001585815,"threshold_uncertainty_score":0.005305052,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03123325241886938,"score_gpt":0.2762630240232856,"score_spread":0.2450297716044162,"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."}}