{"paper":{"title":"Dendrites and chaos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Tomasz Drwi\\k{e}ga","submitted_at":"2017-06-04T15:11:43Z","abstract_excerpt":"We answer the two questions left open in [Z.~Ko\\v{c}an, Internat. J. Bifur. Chaos Appl. Sci. Engrg. \\textbf{22}, article id: 125025 (2012)] i.e. whether there is a relation between $\\omega$-chaos and distributional chaos and whether there is a relation between an infinite LY-scrambled set and distributional chaos for dendrite maps. We construct a continuous self-map of dendrite without any \\textit{DC3} pairs but containing an uncountable $\\omega$-scrambled set. To answer for the second question we construct dendrite $\\mathcal{D}$ and continuous dendrite map without an infinite LY-scrambled set"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01088","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"}