{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:34:48Z","timestamp":1787337288395,"version":"build-2736575974"},"reference-count":26,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>An algorithm for detecting periodic orbits in chaotic systems [R. L. Davidchack and Y.\u2010C. Lai, Phys. Rev. E (3), 60 (1999), pp. 6172\u20136175], which combines the set of stabilizing transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp. 4733\u20134736] with a modified semi\u2010implicit Euler iterative scheme and seeding with periodic orbits of neighboring periods, has been shown to be highly efficient when applied to low\u2010dimensional systems. The difficulty in applying the algorithm to higher\u2010dimensional systems is mainly due to the fact that the number of the stabilizing transformations grows extremely fast with increasing system dimension. Here we analyze the properties of stabilizing transformations and propose an alternative approach for constructing a smaller set of transformations. The performance of the new approach is illustrated on the four\u2010dimensional kicked double rotor map and the six\u2010dimensional system of three coupled H\u00e9non maps.<\/jats:p>","DOI":"10.1137\/050623401","type":"journal-article","created":{"date-parts":[[2006,8,24]],"date-time":"2006-08-24T15:30:58Z","timestamp":1156433458000},"page":"1275-1288","source":"Crossref","is-referenced-by-count":10,"title":["Efficient Detection of Periodic Orbits in Chaotic Systems by Stabilizing Transformations"],"prefix":"10.1137","volume":"28","author":[{"given":"Jonathan J.","family":"Crofts","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruslan L.","family":"Davidchack","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.63.819"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.79.3787"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(91)90227-Z"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.60.6172"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.61.1353"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(01)00463-7"},{"key":"R7","unstructured":"R. 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