{"paper":{"title":"Multiple Periodic Solutions for $\\Gamma$-symmetric Newtonian Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hao-pin Wu, Mieczyslaw Dabkowski, Wieslaw Krawcewicz, Yanli Lv","submitted_at":"2016-12-23T05:13:36Z","abstract_excerpt":"The existence of periodic solutions in $\\Gamma$-symmetric Newtonian systems $\\ddot{x}=-\\nabla f(x)$ can be effectively studied by means of the $(\\Gamma\\times O(2))$-equivariant gradient degree with values in the Euler ring $U(\\Gamma\\times O(2))$. In this paper, we show that in the case of $\\Gamma$ being a finite group, the Euler ring $U(\\Gamma\\times O(2))$ and the related basic degrees are effectively computable using Euler ring homomorphisms, the Burnside ring $A(\\Gamma\\times O(2))$ and the reduced $(\\Gamma\\times O(2))$-degree with no free parameters. We present several examples of Newtonian "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07876","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"}