{"paper":{"title":"Rigorous numerics for a singular perturbation problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Aleksander Czechowski","submitted_at":"2019-09-11T18:21:00Z","abstract_excerpt":"Fast-slow systems are notoriously difficult to analyze with rigorous numerics, since the qualitative properties of the solution space change fundamentally when the so-called small parameter $\\epsilon$ is varied from 0 to small non-zero values. In this dissertation I develop a computer-assisted rigorous method which can be used in combination with topological tools for proving the existence of period and connecting orbits in the near-zero parameter regime. As an application, I prove the existence of periodic and homoclinic orbits in the FitzHugh-Nagumo system, for $\\epsilon \\in (0,\\epsilon_0]$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.06207","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.06207/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}