{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T11:37:21Z","timestamp":1773229041688,"version":"3.50.1"},"reference-count":23,"publisher":"World Scientific Pub Co Pte Lt","issue":"05n06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2005,10]]},"abstract":"<jats:p> We analyze the structure of the frequency spaceQ(F) of a nonabelian free group F = F(a<jats:sub>1<\/jats:sub>,\u2026,a<jats:sub>k<\/jats:sub>) consisting of all shift-invariant Borel probability measures on \u2202F and construct a natural action of Out(F) on Q(F). In particular we prove that for any outer automorphism \u03d5 of F the conjugacy distortion spectrum of \u03d5, consisting of all numbers \u2016\u03d5(w)\u2016\/\u2016w\u2016, where w is a nontrivial conjugacy class, is the intersection of \u211a and a closed subinterval of \u211d with rational endpoints. <\/jats:p>","DOI":"10.1142\/s0218196705002700","type":"journal-article","created":{"date-parts":[[2006,1,4]],"date-time":"2006-01-04T19:48:36Z","timestamp":1136404116000},"page":"939-969","source":"Crossref","is-referenced-by-count":25,"title":["THE FREQUENCY SPACE OF A FREE GROUP"],"prefix":"10.1142","volume":"15","author":[{"given":"ILYA","family":"KAPOVICH","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/PL00001618"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.4310\/jdg\/1214447806"},{"key":"rf3","doi-asserted-by":"crossref","first-page":"783","DOI":"10.4310\/jdg\/1214458531","volume":"43","author":"Bestvina M.","journal-title":"J. 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M.\u00a0Burger and A.\u00a0Iozzi (Springer, 2001)\u00a0pp. 149\u2013166.","DOI":"10.1007\/978-3-662-04743-9_7"},{"key":"rf13","first-page":"263","volume":"49","author":"Gautero F.","journal-title":"Enseign. Math. (2)"},{"key":"rf14","author":"Kaimanovich V.","journal-title":"Israel J. Math."},{"key":"rf15","author":"Kapovich I.","journal-title":"Pacific J. Math."},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-4844-2"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511809187"},{"key":"rf18","first-page":"59","volume":"2","author":"Levitt G.","journal-title":"J. Inst. Math. Jussieu"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61896-3"},{"key":"rf20","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1017\/S014338570000804X","volume":"14","author":"Lyons R.","journal-title":"Ergodic Theory Dynam. 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