{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,15]],"date-time":"2024-01-15T00:05:24Z","timestamp":1705277124392},"reference-count":6,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2004,7]]},"abstract":"<jats:p>We consider the behavior of piecewise isometries in Euclidean spaces. We show that if n is odd and the system contains no orientation reversing isometries then recurrent orbits with rational coding are not expected. More precisely, a prevalent set of piecewise isometries do not have recurrent points having rational coding. This implies that when all atoms are convex no periodic points exist for almost every piecewise isometry.<\/jats:p><jats:p>By contrast, if n\u22652 is even then periodic points are stable for almost every piecewise isometry whose set of defining isometries are not orientation reversing. If, in addition, the defining isometries satisfy an incommensurability condition then all unbounded orbits must be irrationally coded.<\/jats:p>","DOI":"10.1142\/s0218127404010813","type":"journal-article","created":{"date-parts":[[2004,8,23]],"date-time":"2004-08-23T11:43:25Z","timestamp":1093261405000},"page":"2353-2361","source":"Crossref","is-referenced-by-count":5,"title":["PERIODICITY AND RECURRENCE IN PIECEWISE ROTATIONS OF EUCLIDEAN SPACES"],"prefix":"10.1142","volume":"14","author":[{"given":"MIGUEL","family":"MENDES","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of Surrey, Guildford, GU2 7XH, UK"}]},{"given":"MATTHEW","family":"NICOL","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Surrey, Guildford, GU2 7XH, UK"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/10\/3\/002"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.1998.4.593"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/14\/2\/302"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511569333"},{"key":"rf6","volume-title":"Higher Algebra","author":"Mishina A.","year":"1965"},{"key":"rf8","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198531470.001.0001","volume-title":"Convexity","author":"Webster R.","year":"1994"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127404010813","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,14]],"date-time":"2024-01-14T06:39:48Z","timestamp":1705214388000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127404010813"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,7]]},"references-count":6,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2004,7]]}},"alternative-id":["10.1142\/S0218127404010813"],"URL":"https:\/\/doi.org\/10.1142\/s0218127404010813","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,7]]}}}