{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T05:39:17Z","timestamp":1772516357211,"version":"3.50.1"},"reference-count":13,"publisher":"Wiley","license":[{"start":{"date-parts":[[2012,12,1]],"date-time":"2012-12-01T00:00:00Z","timestamp":1354320000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We present a practical algorithm to compute models of rational functions with minimal resultant under conjugation by fractional linear transformations. We also report on a search for rational functions of degrees 2 and 3 with rational coefficients that have many integers in a single orbit. We find several minimal quadratic rational functions with eight integers in an orbit and several minimal cubic rational functions with ten integers in an orbit. We also make some elementary observations on possibilities of an analogue of Szpiro\u2019s conjecture in a dynamical setting and on the structure of the set of minimal models for a given rational function.<\/jats:p>","DOI":"10.1112\/s1461157012001131","type":"journal-article","created":{"date-parts":[[2012,12,19]],"date-time":"2012-12-19T14:55:11Z","timestamp":1355928911000},"page":"400-417","source":"Crossref","is-referenced-by-count":2,"title":["Minimal models for rational functions in a dynamical setting"],"prefix":"10.1112","volume":"15","author":[{"given":"Nils","family":"Bruin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Molnar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2012,12,1]]},"reference":[{"key":"S1461157012001131_ref8","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-93-07129-3"},{"key":"S1461157012001131_ref6","unstructured":"[6] Molnar A. , \u2018Fractional linear minimal models of rational functions\u2019, MSc\u00a0Thesis, Simon Fraser University, 2011."},{"key":"S1461157012001131_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-69904-2"},{"key":"S1461157012001131_ref3","unstructured":"[3] Bruin N. and Molnar A. , \u2018Integers in orbits of rational functions \u2019, 2012, http:\/\/www.cecm.sfu.ca\/\u223cnbruin\/intorbits."},{"key":"S1461157012001131_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0097582"},{"key":"S1461157012001131_ref7","doi-asserted-by":"publisher","DOI":"10.1155\/S1073792894000127"},{"key":"S1461157012001131_ref5","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s2-39.1.431"},{"key":"S1461157012001131_ref1","unstructured":"[1] Behnel S. , Bradshaw R. , Ewing G. , Seljebotn D. S. et al., \u2018Cython: C-extensions for python\u2019, 2009, http:\/\/www.cython.org."},{"key":"S1461157012001131_ref11","unstructured":"[11] Stein W.\u00a0A. , \u2018Sage Mathematics Software (Version 4.7)\u2019, The Sage Development Team, 2011, http:\/\/www.sagemath.org."},{"key":"S1461157012001131_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-07010-9"},{"key":"S1461157012001131_ref12","unstructured":"[12] Szpiro L. , Tepper M. and Williams P. , \u2018Resultant and conductor of geometrically semi-stable self maps of the projective line over a number field or function field\u2019, Preprint, 2010, http:\/\/arxiv.org\/abs\/1010.5030."},{"key":"S1461157012001131_ref9","first-page":"269","article-title":"The field of definition for dynamical systems on P1","volume":"98","author":"Silverman","year":"1995","journal-title":"Compositio Math."},{"key":"S1461157012001131_ref2","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1996.0125"}],"container-title":["LMS Journal of Computation and Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1461157012001131","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,7]],"date-time":"2019-06-07T00:47:25Z","timestamp":1559868445000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1461157012001131\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12,1]]},"references-count":13,"alternative-id":["S1461157012001131"],"URL":"https:\/\/doi.org\/10.1112\/s1461157012001131","relation":{},"ISSN":["1461-1570"],"issn-type":[{"value":"1461-1570","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12,1]]}}}