{"paper":{"title":"Pruning fronts and the formation of horseshoes","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Andre de Carvalho","submitted_at":"1997-01-15T00:00:00Z","abstract_excerpt":"Let f:E -> E be a homeomorphism of the plane E. We define open sets P, called {\\em pruning fronts} after the work of Cvitanovi\\'c, for which it is possible to construct an isotopy H: E x [0,1] -> E with open support contained in the union of f^{n}(P), such that H(*,0)=f(*) and H(*,1)=f_P(*), where f_P is a homeomorphism under which every point of P is wandering. Applying this construction with f being Smale's horseshoe, it is possible to obtain an uncountable family of homeomorphisms, depending on infinitely many parameters, going from trivial to chaotic dynamic behaviour. This family is a 2-d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9701217","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"}