{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:53:18Z","timestamp":1772293998108,"version":"3.50.1"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2012,11]]},"abstract":"<jats:p> We explore the relationship between the limit spaces of contracting self-similar groups and self-similar structures. We give the condition on a contracting group such that its limit space admits a self-similar structure, and also the condition such that this self-similar structure is post-critically finite (p.c.f.). We then give necessary and sufficient conditions for a p.c.f. self-similar structure to be the limit space of a contracting self-similar group. When these conditions hold we give a construction of the contracting group. Finally, we illustrate our results with several examples. <\/jats:p>","DOI":"10.1142\/s0218196712500567","type":"journal-article","created":{"date-parts":[[2012,6,27]],"date-time":"2012-06-27T23:45:57Z","timestamp":1340840757000},"page":"1250056","source":"Crossref","is-referenced-by-count":6,"title":["FROM SELF-SIMILAR STRUCTURES TO SELF-SIMILAR GROUPS"],"prefix":"10.1142","volume":"22","author":[{"given":"DANIEL J.","family":"KELLEHER","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Connecticut, Storrs, CT 06269, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"BENJAMIN A.","family":"STEINHURST","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Cornell University, Ithaca, NY 14853, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"CHUEN-MING M.","family":"WONG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Columbia University, New York, NY 10027, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,12,3]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8014-5_2"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/S1570-7954(03)80078-5"},{"key":"rf4","first-page":"21","volume":"2","author":"Bondarenko E.","journal-title":"Algebra Discrete Math."},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1201\/9781439865699"},{"key":"rf6","first-page":"53","volume":"14","author":"Grigorchuk R. I.","journal-title":"Funktsional. Anal. i Prilozhen."},{"key":"rf7","first-page":"939","volume":"48","author":"Grigorchuk R. I.","journal-title":"Izv. Akad. Nauk SSSR Ser. Mat."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/077\/2459869"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2006.02.001"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/BF01179757"},{"key":"rf11","first-page":"721","volume":"335","author":"Kigami J.","journal-title":"Trans. Amer. Math. Soc."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511470943"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511842467.004"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/117"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/077\/2459868"},{"key":"rf16","doi-asserted-by":"crossref","DOI":"10.1515\/9780691186832","volume-title":"Differential Equations on Fractals","author":"Strichartz R. S.","year":"2006"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1007\/s10711-006-9106-8"},{"key":"rf18","volume-title":"A New Kind of Science","author":"Wolfram S.","year":"2002"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196712500567","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T08:31:54Z","timestamp":1565166714000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196712500567"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11]]},"references-count":17,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2012,12,3]]},"published-print":{"date-parts":[[2012,11]]}},"alternative-id":["10.1142\/S0218196712500567"],"URL":"https:\/\/doi.org\/10.1142\/s0218196712500567","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,11]]}}}