{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T22:20:27Z","timestamp":1780957227876,"version":"3.54.1"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2007,6]]},"abstract":"<jats:p> This paper focuses on resonance phenomena that occur in a vicinity of a linear degeneracy corresponding to a triple-zero eigenvalue of an equilibrium point in an autonomous tridimensional system. Namely, by means of blow-up techniques that relate the triple-zero bifurcation to the Kuramoto\u2013Sivashinsky system, we characterize the resonances that appear near the triple-zero bifurcation. <\/jats:p><jats:p> Using numerical tools, the results are applied to the R\u00f6ssler equation, showing a number of interesting bifurcation behaviors associated to these resonance phenomena. In particular, the merging of the periodic orbits appeared in resonances, the existence of two types of Takens\u2013Bogdanov bifurcations of periodic orbits and the presence of Feigenbaum cascades of these bifurcations, joined by invariant tori curves, are pointed out. <\/jats:p>","DOI":"10.1142\/s0218127407018178","type":"journal-article","created":{"date-parts":[[2007,9,4]],"date-time":"2007-09-04T07:33:08Z","timestamp":1188891188000},"page":"1997-2008","source":"Crossref","is-referenced-by-count":14,"title":["RESONANCES OF PERIODIC ORBITS IN R\u00d6SSLER SYSTEM IN PRESENCE OF A TRIPLE-ZERO BIFURCATION"],"prefix":"10.1142","volume":"17","author":[{"given":"ANTONIO","family":"ALGABA","sequence":"first","affiliation":[{"name":"Department of Mathematics, Facultad de Ciencias Experimentales, Univ. Huelva Avda. de las Fuerzas Armadas s\/n, 21071-Huelva, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"EMILIO","family":"FREIRE","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics II, E.T.S. Ingenieros, Univ. Sevilla, Camino de los Descubrimientos s\/n, 41092-Sevilla, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"ESTANISLAO","family":"GAMERO","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics II, E.T.S. Ingenieros, Univ. Sevilla, Camino de los Descubrimientos s\/n, 41092-Sevilla, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"ALEJANDRO J.","family":"RODR\u00cdGUEZ-LUIS","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics II, E.T.S. Ingenieros, Univ. Sevilla, Camino de los Descubrimientos s\/n, 41092-Sevilla, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127498001583"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127403006741"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-0147-9"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511665639"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1080\/02681110010017417"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402006175"},{"key":"rf10","series-title":"Appl. Math. Sci. Series","volume-title":"Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields","volume":"42","author":"Guckenheimer J.","year":"1997"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/4\/4\/002"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(93)90069-D"},{"key":"rf13","series-title":"Appl. Math. Sci. Series","volume-title":"Elements of Applied Bifurcation Theory","volume":"112","author":"Kuznetsov Yu. A.","year":"1998"},{"key":"rf14","series-title":"Advanced Series in Nonlinear Dynamics","doi-asserted-by":"crossref","DOI":"10.1142\/2001","volume-title":"Renormalisation in Area-Preserving Maps","volume":"6","author":"Mackay R. S.","year":"1993"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(86)90110-1"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(86)90055-2"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1111\/j.1749-6632.1979.tb29482.x"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/17\/1\/006"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-0374-9"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127407018178","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T10:58:03Z","timestamp":1565175483000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127407018178"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,6]]},"references-count":16,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2007,6]]}},"alternative-id":["10.1142\/S0218127407018178"],"URL":"https:\/\/doi.org\/10.1142\/s0218127407018178","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,6]]}}}