{"paper":{"title":"The Conley index for discrete dynamical systems and the mapping torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.DS","authors_text":"Frank Weilandt","submitted_at":"2018-01-19T13:55:28Z","abstract_excerpt":"The Conley index for flows is a topological invariant describing the behavior around an isolated invariant set $S$. It is defined as the homotopy type of a quotient space $N/L$, where $(N,L)$ is an index pair for $S$. In the case of a discrete dynamical system, i.e., a continuous self-map $f\\colon X\\to X$, the definition is similar. But one needs to consider the index map $f_{(N,L)}\\colon N/L\\to N/L$ induced by $f$. The Conley index in this situation is defined as the homotopy class $[f_{(N,L)}]$ modulo shift equivalence. The shift equivalence relation is rarely used outside this context and n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06403","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":""},"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"}