{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T13:58:43Z","timestamp":1772287123915,"version":"3.50.1"},"reference-count":26,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2013,11]]},"abstract":"<jats:p> We face the problem of characterizing the periodic cases in parametric families of rational diffeomorphisms of \ud835\udd42<jats:sup>k<\/jats:sup>, where \ud835\udd42 is \u211d or \u2102, having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two- and three-dimensional classes of polynomial or rational maps. In particular, we find the global periodic cases for several Lyness-type recurrences. <\/jats:p>","DOI":"10.1142\/s0218127413501824","type":"journal-article","created":{"date-parts":[[2013,12,13]],"date-time":"2013-12-13T02:07:05Z","timestamp":1386900425000},"page":"1350182","source":"Crossref","is-referenced-by-count":5,"title":["GLOBAL PERIODICITY CONDITIONS FOR MAPS AND RECURRENCES VIA NORMAL FORMS"],"prefix":"10.1142","volume":"23","author":[{"given":"ANNA","family":"CIMA","sequence":"first","affiliation":[{"name":"Departament de Matem\u00e0tiques, Facultat de Ci\u00e8ncies, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ARMENGOL","family":"GASULL","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tiques, Facultat de Ci\u00e8ncies, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V\u00cdCTOR","family":"MA\u00d1OSA","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tica Aplicada III (MA3), Control, Dynamics and Applications Group (CoDALab), Universitat Polit\u00e8cnica de Catalunya (UPC), Colom 1, 08222 Terrassa, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,12,12]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-247X(03)00272-5"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2005.11.022"},{"key":"rf3","volume-title":"An Introduction to Dynamical Systems","author":"Arrowsmith D. 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