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The method uses a rotation-angle representation constructed with delay coordinates, estimates rotation numbers with an evaluated error bound, determines resonance mode numbers of island chains, and classifies orbit types through sparse sampling of the waveform of the rotation angle. Validity tests were performed using the standard map, with benchmarks against widely used methods. We also present a practical application to the magnetic field in the toroidal plasma confinement device Heliotron J. We found that the method achieves accurate extraction of topological information, despite its limitations in certain cases.<\/jats:p>","DOI":"10.1063\/5.0336427","type":"journal-article","created":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T12:48:00Z","timestamp":1791377280000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Identification of topological information from orbits in area-preserving maps"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9118-5765","authenticated-orcid":false,"given":"F.","family":"Cai","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7787-3307","authenticated-orcid":false,"given":"S.","family":"Kado","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9117-5898","authenticated-orcid":false,"given":"G.","family":"Kawamura","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,10,7]]},"reference":[{"issue":"2","key":"2026100708475324800_c1","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1007\/s40295-015-0042-4","article-title":"Enhanced visualization and autonomous extraction of Poincar\u00e9 map topology","volume":"61","year":"2014","journal-title":"J. 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