{"paper":{"title":"Degree counting for Toda system with simple singularity : one point blow up","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chang-shou Lin, Lei Zhang, Wen Yang, Youngae Lee","submitted_at":"2017-07-22T12:53:14Z","abstract_excerpt":"In this paper, we study the degree counting formula of the rank two Toda system with simple singular source when $\\rho_1\\in(0,4\\pi)\\cup(4\\pi,8\\pi)$ and $\\rho_2\\notin 4\\pi\\mathbb{N}.$ The key step is to derive the degree formula of the shadow system, which arises from the bubbling solutions as $\\rho_1$ tends to $4\\pi$. In order to compute the topological degree of the shadow system, we need to find some suitable deformation. During this deformation, we shall deal with \\textit{new} difficulty arising from the new phenomena: blow up does not necessarily imply concentration of mass. This phenomena"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07156","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"}