{"id":"W4412830928","doi":"10.1007/s00220-025-05381-8","title":"On a Countable Sequence of Homoclinic Orbits Arising Near a Saddle–Center Point","year":2025,"lang":"en","type":"article","venue":"Communications in Mathematical Physics","topic":"Nonlinear Waves and Solitons","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"H2020 European Research Council; Agencia Estatal de Investigación; Universitat de Barcelona; European Regional Development Fund; Institució Catalana de Recerca i Estudis Avançats; European Commission","keywords":"Homoclinic orbit; Countable set; Saddle; Saddle point; Sequence (biology); Mathematics; Center (category theory); Homoclinic bifurcation; Point (geometry); Mathematical analysis; Pure mathematics; Geometry; Physics; Nonlinear system; Bifurcation; Quantum mechanics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006978029,0.0005870417,0.0006290561,0.002119627,0.001578544,0.001409488,0.0008670635,0.0007681985,0.002389732],"category_scores_gemma":[0.002420955,0.0003561183,0.0007426997,0.0007860291,0.002435639,0.001678917,0.001316489,0.001076757,0.0003083722],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009714919,"about_ca_system_score_gemma":0.0004835821,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007597763,"about_ca_topic_score_gemma":0.000968511,"domain_scores_codex":[0.9997392,0.00005886149,0.00002006442,0.00005126797,0.0000914512,0.00003916588],"domain_scores_gemma":[0.9988009,0.0004988984,0.000244675,0.0001343121,0.0001622163,0.0001590581],"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":[0.0000628648,0.00004628451,0.001603104,0.000129684,0.00002778267,0.0008453904,0.0004331746,0.01210815,0.01150501,0.9658877,0.0005608502,0.006790005],"study_design_scores_gemma":[0.00004286291,0.0001011191,0.002214581,0.0001019239,0.0000213933,0.0008888126,0.0003046075,0.2095695,0.004387704,0.7807069,0.001615284,0.00004532955],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8556376,0.0003263621,0.1245472,0.0003568326,0.00004389624,0.00004399662,0.0001087365,0.000143521,0.01879195],"genre_scores_gemma":[0.9696546,0.0003126536,0.02498344,0.00005574882,0.00003775847,0.00006274361,0.0002020629,0.00004973321,0.004641228],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002389732,"threshold_uncertainty_score":0.007994413,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05516049042890177,"score_gpt":0.3796004943491132,"score_spread":0.3244400039202115,"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."}}