{
  "annotation_id": "5dbd904d-9231-4ff6-8825-0a9334335e25",
  "date_created": "2026-02-17T05:53:16.199000Z",
  "date_modified": "2026-02-17T05:53:16.199000Z",
  "file_hash": "62ad3a59c317421c3791421be30dde8b8b958d9c488ecbdefac6ff1b210c2a81",
  "private": false,
  "record": {
    "abstract": "This paper examines the relationship between shadowing phenomena and the continuity properties of $\\omega$-limit sets in dynamical systems. We give a necessary and sufficient condition for a shadowable point to be an upper (resp. a lower) semicontinuity point of $\\omega$-limit sets. Assuming global shadowing, we show that the lower semicontinuity of $\\omega$-limit sets is equivalent to the chain continuity. We also show that the lower semicontinuity of $\\omega$-limit sets is equivalent to the chain continuity in a general setting. Several examples are given to illustrate the results.",
    "arxiv_id": "2601.08407",
    "authors": [
      "Noriaki Kawaguchi"
    ],
    "categories": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Shadowing and the continuity of omega-limit sets",
    "url": "https://arxiv.org/abs/2601.08407",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "77b38189-92dd-4305-994d-ca295b361320",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}