{"id":"W2963871217","doi":"10.1016/j.jmaa.2017.02.064","title":"Nonuniform (h,k,μ,ν)-dichotomy with applications to nonautonomous dynamical systems","year":2017,"lang":"en","type":"article","venue":"Journal of Mathematical Analysis and Applications","topic":"Stability and Controllability of Differential Equations","field":"Engineering","cited_by":13,"is_retracted":false,"has_abstract":false,"ca_institutions":"York University","funders":"Canadian Institutes of Health Research; Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Mathematics; Linear subspace; Dynamical systems theory; Lyapunov exponent; Pure mathematics; Lyapunov function; Invariant (physics); Exponential dichotomy; Implicit function theorem; Banach space; Linear system; Discrete mathematics; Mathematical analysis; Differential equation; Nonlinear system","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007514209,0.0004033306,0.0008525256,0.0009233169,0.001035306,0.00116983,0.0005725711,0.0007299487,0.002396919],"category_scores_gemma":[0.002609105,0.0001928112,0.0005629489,0.0005454916,0.001730964,0.001424613,0.002065378,0.001076108,0.00009671156],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000906602,"about_ca_system_score_gemma":0.000609867,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007545559,"about_ca_topic_score_gemma":0.0005131583,"domain_scores_codex":[0.9998035,0.00005733814,0.0000145924,0.00004724867,0.00003844511,0.00003890174],"domain_scores_gemma":[0.9988769,0.0005655425,0.0001522771,0.00005650153,0.0001428143,0.0002060183],"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":[0.0001168225,0.00004442553,0.001197009,0.00009186602,0.00002736391,0.0002784793,0.0002022615,0.02306352,0.004183726,0.9627569,0.001213976,0.006823668],"study_design_scores_gemma":[0.00003684299,0.00007543429,0.00124558,0.00002284581,0.00001514802,0.0001558131,0.0001668207,0.3348073,0.0007886662,0.660971,0.001688623,0.00002602215],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.627956,0.002658012,0.3238864,0.003801991,0.0005792649,0.00006679076,0.0003911672,0.0001597372,0.0405006],"genre_scores_gemma":[0.9851314,0.0006571307,0.009996481,0.0001548169,0.0002039576,0.00004342739,0.00006814037,0.00001507886,0.003729613],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002396919,"threshold_uncertainty_score":0.008018494,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009281943521272347,"score_gpt":0.2436588225441084,"score_spread":0.234376879022836,"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."}}