{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T20:47:44Z","timestamp":1759092464750},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,9]]},"abstract":"<jats:p> The standard map x\u2032 = x + y\u2032, y\u2032 = y + (K\/2\u03c0) sin (2\u03c0x), where both x and y are given modulo 1, becomes mostly chaotic for K \u2265 8, but important islands of stability appear in a recurrent way for values of K near K = 2n\u03c0 (groups of islands I and II), and K = (2n + 1)\u03c0 (group III), where n \u2265 1. The maximum areas of the islands and the intervals \u0394K, where the islands appear, follow power laws. The changes of the areas of the islands around a maximum follow universal patterns. All islands surround stable periodic orbits. Most of the orbits are irregular, i.e. unrelated to the orbits of the unperturbed problem K = 0. The main periodic orbits of periods 1, 2 and 4 and their stability are derived analytically. As K increases these orbits become unstable and they are followed by infinite period-doubling bifurcations with a bifurcation ratio \u03b4 = 8.72. We find theoretically the connections between the various families and the extent of their stability. Numerical calculations verify the theoretical results. <\/jats:p>","DOI":"10.1142\/s021812740501371x","type":"journal-article","created":{"date-parts":[[2005,10,26]],"date-time":"2005-10-26T11:55:00Z","timestamp":1130327700000},"page":"2865-2882","source":"Crossref","is-referenced-by-count":11,"title":["RECURRENCE OF ORDER IN CHAOS"],"prefix":"10.1142","volume":"15","author":[{"given":"G.","family":"CONTOPOULOS","sequence":"first","affiliation":[{"name":"Academy of Athens, Research Center of Astronomy, 4 Soranou Efessiou Str. 11527 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"HARSOULA","sequence":"additional","affiliation":[{"name":"Academy of Athens, Research Center of Astronomy, 4 Soranou Efessiou Str. 11527 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R.","family":"DVORAK","sequence":"additional","affiliation":[{"name":"Universit\u00e4t Wien, Institut f\u00fcr Astronomie, T\u00fcrkenschanzstrasse 17, A-1180 Wien, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F.","family":"FREISTETTER","sequence":"additional","affiliation":[{"name":"Universit\u00e4t Wien, Institut f\u00fcr Astronomie, T\u00fcrkenschanzstrasse 17, A-1180 Wien, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02776065"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0370-1573(79)90023-1"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1086\/110948"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/32\/28\/303"},{"key":"rf5","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/S0294-1449(16)30180-9","volume":"11","author":"Duarte P.","journal-title":"Ann. Inst. Henri Poincar\u00e9"},{"key":"rf6","first-page":"359","volume":"259","author":"Giorgilli A.","journal-title":"Phys. Lett. A"},{"key":"rf7","first-page":"992","volume":"28","author":"H\u00e9non M.","journal-title":"Ann. Astrophys."},{"key":"rf8","first-page":"57","volume":"1","author":"H\u00e9non M.","journal-title":"Bull Astron."},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(82)90045-8"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2184-3"},{"key":"rf11","unstructured":"S. E.\u00a0Newhouse, Chaotic Behaviour of Deterministic Systems, eds. G.\u00a0Looss, R. H. G.\u00a0Helleman and R.\u00a0Stora (North Holland, Amsterdam, 1983)\u00a0pp. 443\u2013451."},{"key":"rf12","volume-title":"Numerical Recipes in Fortran","author":"Press W. H.","year":"1992"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1063\/1.166444"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1063\/1.166252"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/S0370-1573(02)00331-9"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021812740501371X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:09:20Z","timestamp":1565136560000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021812740501371X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,9]]},"references-count":15,"journal-issue":{"issue":"09","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,9]]}},"alternative-id":["10.1142\/S021812740501371X"],"URL":"https:\/\/doi.org\/10.1142\/s021812740501371x","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,9]]}}}