{"paper":{"title":"Regular dependence of the Peierls barriers on perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Chong-Qing Cheng, Qinbo Chen","submitted_at":"2016-12-22T02:52:30Z","abstract_excerpt":"Let $f$ be an exact area-preserving monotone twist diffeomorphism of the infinite cylinder and $P_{\\omega,f}(\\xi)$ be the associated Peierls barrier. In this paper, we give the H\\\"{o}lder regularity of $P_{\\omega,f}(\\xi)$ with respect to the parameter $f$. In fact, we prove that if the rotation symbol $\\omega\\in (\\mathbb{R}\\setminus\\mathbb{Q})\\bigcup(\\mathbb{Q}+)\\bigcup(\\mathbb{Q}-)$, then $P_{\\omega,f}(\\xi)$ is $1/3$-H\\\"{o}lder continuous in $f$, i.e. $$|P_{\\omega,f'}(\\xi)-P_{\\omega,f}(\\xi)|\\leq C\\|f'-f\\|_{C^1}^{1/3} ,~~\\forall \\xi\\in\\mathbb{R}$$ where $C$ is a constant. Similar results also "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07422","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"}