{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,9]],"date-time":"2025-12-09T04:12:27Z","timestamp":1765253547014},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2012,5]]},"abstract":"<jats:p> We say a subset \u03a3 \u2286 F<jats:sub>N<\/jats:sub> of the free group of rank N is spectrally rigid if whenever T<jats:sub>1<\/jats:sub>, T<jats:sub>2<\/jats:sub> \u2208 cv <jats:sub>N<\/jats:sub> are \u211d-trees in (unprojectivized) outer space for which \u2016\u03c3\u2016<jats:sub>T<jats:sub>1<\/jats:sub><\/jats:sub> = \u2016\u03c3\u2016<jats:sub>T<jats:sub>2<\/jats:sub><\/jats:sub> for every \u03c3 \u2208 \u03a3, then T<jats:sub>1<\/jats:sub> = T<jats:sub>2<\/jats:sub> in cv <jats:sub>N<\/jats:sub>. The general theory of (non-abelian) actions of groups on \u211d-trees establishes that T \u2208 cv <jats:sub>N<\/jats:sub> is uniquely determined by its translation length function \u2016\u22c5\u2016<jats:sub>T<\/jats:sub> : F<jats:sub>N<\/jats:sub> \u2192 \u211d, and consequently that F<jats:sub>N<\/jats:sub> itself is spectrally rigid. Results of Smillie and Vogtmann, and of Cohen, Lustig and Steiner establish that no finite \u03a3 is spectrally rigid. Capitalizing on their constructions, we prove that for any \u03a6 \u2208 Aut (F<jats:sub>N<\/jats:sub>) and g \u2208 F<jats:sub>N<\/jats:sub>, the set \u03a3 = {\u03a6<jats:sup>n<\/jats:sup>(g)}<jats:sub>n\u2208\u2124<\/jats:sub> is not spectrally rigid. <\/jats:p>","DOI":"10.1142\/s021819671250021x","type":"journal-article","created":{"date-parts":[[2011,11,14]],"date-time":"2011-11-14T01:19:47Z","timestamp":1321233587000},"page":"1250021","source":"Crossref","is-referenced-by-count":2,"title":["NON-RIGIDITY OF CYCLIC AUTOMORPHIC ORBITS IN FREE GROUPS"],"prefix":"10.1142","volume":"22","author":[{"given":"BRIAN","family":"RAY","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,5,6]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.2307\/121043"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.2307\/2946562"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.4171\/041"},{"key":"rf5","doi-asserted-by":"crossref","DOI":"10.1142\/4495","volume-title":"Introduction to \u039b-Trees","author":"Chiswell I.","year":"2001"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3142-4_7"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(87)90229-8"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-74614-2"},{"key":"rf10","first-page":"485","volume":"39","author":"Smillie J.","journal-title":"Michigan Math. J."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021819671250021X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:03:28Z","timestamp":1565121808000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021819671250021X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,5]]},"references-count":8,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2012,5,6]]},"published-print":{"date-parts":[[2012,5]]}},"alternative-id":["10.1142\/S021819671250021X"],"URL":"https:\/\/doi.org\/10.1142\/s021819671250021x","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,5]]}}}