{"paper":{"title":"On the Dynamics of Invariant Graphs for Dissipative Twist Maps","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DS","authors_text":"Lin Wang, Qi Li","submitted_at":"2025-06-05T12:14:35Z","abstract_excerpt":"For two-parameter families of dissipative twist maps, we investigate the dynamics of invariant graphs as well as the thresholds for their existence and breakdown. Our main results are as follows:\n  (1) For arbitrarily small $C^r$ perturbations with $r \\geq 1$, invariant graphs with prescribed rotation numbers can be realized by adjusting the parameters;\n  (2) We characterize sharp perturbations that lead to the complete destruction of all invariant graphs;\n  (3) When the perturbation fails to be $C^1$, Lipschitz invariant graphs with non-differentiable points may still persist, even though the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04938","kind":"arxiv","version":2},"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/2506.04938/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"}