{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T06:08:19Z","timestamp":1762322899641},"reference-count":2,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2003,10]]},"abstract":"<jats:p> We prove that for \u03bb\u22651 and all sufficiently large \u220a, the set of (\u03bb,\u220a)-quasigeodesics in an infinite word-hyperbolic group G is regular if and only if \u03bb is rational. In fact, this set of quasigeodesics defines an asynchronous automatic structure for G. We also introduce the idea of an exact (\u03bb,\u220a)-quasigeodesic and show that for rational \u03bb and appropriate \u220a the sets of exact (\u03bb,\u220a)-quasigeodesics define synchronous automatic structures. <\/jats:p>","DOI":"10.1142\/s0218196703001560","type":"journal-article","created":{"date-parts":[[2004,1,13]],"date-time":"2004-01-13T04:14:02Z","timestamp":1073967242000},"page":"585-596","source":"Crossref","is-referenced-by-count":7,"title":["REGULARITY OF QUASIGEODESICS IN A HYPERBOLIC GROUP"],"prefix":"10.1142","volume":"13","author":[{"given":"DEREK F.","family":"HOLT","sequence":"first","affiliation":[{"name":"Mathematics Institute, University of Warwick,  Coventry CV4 7AL, UK"}]},{"given":"SARAH","family":"REES","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Newcastle,  Newcastle NE1 7RU, UK"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1201\/9781439865699"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/S021819679200027X"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196703001560","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:24:13Z","timestamp":1565115853000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196703001560"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,10]]},"references-count":2,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,10]]}},"alternative-id":["10.1142\/S0218196703001560"],"URL":"https:\/\/doi.org\/10.1142\/s0218196703001560","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,10]]}}}