{"paper":{"title":"Poincar\\'e-Bendixson Theorem for Hybrid Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.OC","nlin.CD"],"primary_cat":"math.DS","authors_text":"Anthony Bloch, Leonardo Colombo, William Clark","submitted_at":"2018-01-27T00:48:09Z","abstract_excerpt":"The Poincar\\'e-Bendixson theorem plays an important role in the study of the qualitative behavior of dynamical systems on the plane; it describes the structure of limit sets in such systems. We prove a version of the Poincar\\'e-Bendixson Theorem for two dimensional hybrid dynamical systems and describe a method for computing the derivative of the Poincar\\'e return map, a useful object for the stability analysis of hybrid systems. We also prove a Poincar\\'e-Bendixson Theorem for a class of one dimensional hybrid dynamical systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09014","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}