{"paper":{"title":"Dynamics on Hyperspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adriano Da Silva, Heriberto Roman-Flores, Victor Ayala","submitted_at":"2018-11-09T17:36:55Z","abstract_excerpt":"Given a compact metric space (X; \\varrho) and a continuous function f:X\\rightarrow X, we study the dynamics of the induced map \\bar{f} on the hyperspace of the compact subsets of X. We show how the chain recurrent set of f and its components are related with the one of the induced map. The main result of the paper proves that, under mild conditions, the numbers of chain components of \\bar{f} is greater than the ones of f. Showing the richness in the dynamics of \\bar{f} which cannot be perceived by f."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04034","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"}