{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T19:18:42Z","timestamp":1774898322858,"version":"3.50.1"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2001,3,7]],"date-time":"2001-03-07T00:00:00Z","timestamp":983923200000},"content-version":"unspecified","delay-in-days":34,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ergod. Th. Dynam. Sys."],"published-print":{"date-parts":[[2001,2]]},"abstract":"<jats:p>We study <jats:italic>\\mathcal{C}^k<\/jats:italic>-diffeomorphisms, <jats:italic>k<\/jats:italic>\\ge 1, <jats:italic>f<\/jats:italic>: M\\to M, exhibiting heterodimensional cycles (i.e. cycles containing periodic points of different stable indices). We prove that if <jats:italic>f<\/jats:italic> can not be <jats:italic>\\mathcal{C}^k<\/jats:italic>-approximated by diffeomorphisms with homoclinic tangencies, then <jats:italic>f<\/jats:italic> is in the closure of an open set <jats:italic>\\mathcal{U}\\subset \\operatorname{Diff}^k(M)<\/jats:italic> consisting of diffeomorphisms <jats:italic>g<\/jats:italic> with a non-hyperbolic transitive set <jats:italic>\\Lambda_g<\/jats:italic> which is locally maximal and strongly partially hyperbolic (the partially hyperbolic splitting at <jats:italic>\\Lambda_g<\/jats:italic> has three non-trivial directions). As a consequence, in the case of 3-manifolds, we give new examples of open sets of <jats:italic>\\mathcal{C}^1<\/jats:italic>-diffeomorphisms for which residually infinitely many sinks or sources coexist (<jats:inline-formula id=\"eq012\">\\mathcal{C}^1<\/jats:inline-formula>-Newhouse's phenomenon). We also prove that the occurrence of non-hyperbolic dynamics has persistent character in the unfolding of heterodimensional cycles.<\/jats:p>","DOI":"10.1017\/s0143385701001067","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T09:39:16Z","timestamp":1027762756000},"page":"25-76","source":"Crossref","is-referenced-by-count":15,"title":["Partially hyperbolic and transitive dynamics generated by heteroclinic cycles"],"prefix":"10.1017","volume":"21","author":[{"given":"LORENZO J.","family":"D\u00cdAZ","sequence":"first","affiliation":[]},{"given":"JORGE","family":"ROCHA","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2001,3,7]]},"container-title":["Ergodic Theory and Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0143385701001067","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,8]],"date-time":"2019-05-08T15:03:37Z","timestamp":1557327817000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0143385701001067\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,2]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2001,2]]}},"alternative-id":["S0143385701001067"],"URL":"https:\/\/doi.org\/10.1017\/s0143385701001067","relation":{},"ISSN":["0143-3857","1469-4417"],"issn-type":[{"value":"0143-3857","type":"print"},{"value":"1469-4417","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,2]]}}}