{"paper":{"title":"Quasi-periodic solutions to nonlinear beam equation on Compact Lie Groups with a multiplicative potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bochao Chen, Shan Jiang, Yixian Gao, Yong Li","submitted_at":"2017-06-15T08:03:18Z","abstract_excerpt":"The goal of this work is to study the existence of quasi-periodic solutions in time to nonlinear beam equations with a multiplicative potential. The nonlinearities are required to only finitely differentiable and the frequency is along a pre-assigned direction. The result holds on any compact Lie group or homogenous manifold with respect to a compact Lie group, which includes the standard torus $\\mathbf{T}^{d}$, the special orthogonal group $SO(d)$, the special unitary group $SU(d)$, the spheres $S^d$ and the real and complex Grassmannians. The proof is based on a differentiable Nash-Moser ite"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04766","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"}