{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:57:59Z","timestamp":1760245079585},"reference-count":25,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2013,4]]},"abstract":"<jats:p> We study the existence of periodic solutions of the nonautonomous periodic Lyness' recurrenceu<jats:sub>n+2<\/jats:sub> = (a<jats:sub>n<\/jats:sub> + u<jats:sub>n+1<\/jats:sub>)\/u<jats:sub>n<\/jats:sub>, where {a<jats:sub>n<\/jats:sub>}<jats:sub>n<\/jats:sub> is a cycle with positive values a, b and with positive initial conditions. It is known that for a = b = 1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a, b) \u2260 (1, 1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a \u2260 b, then any odd period, except 1, appears. <\/jats:p>","DOI":"10.1142\/s0218127413500715","type":"journal-article","created":{"date-parts":[[2013,5,15]],"date-time":"2013-05-15T03:19:19Z","timestamp":1368587959000},"page":"1350071","source":"Crossref","is-referenced-by-count":6,"title":["ON PERIODIC SOLUTIONS OF 2-PERIODIC LYNESS' EQUATIONS"],"prefix":"10.1142","volume":"23","author":[{"given":"GUY","family":"BASTIEN","sequence":"first","affiliation":[{"name":"Institut Math\u00e9matique de Jussieu, Universit\u00e9 Paris 6 and CNRS, 4 pl. 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