{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T09:36:51Z","timestamp":1775036211784,"version":"3.50.1"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Port. Math."],"published-print":{"date-parts":[[2012,6,27]]},"abstract":"<jats:p>\n                    For a map\n                    <jats:inline-formula>\n                      <jats:tex-math>f\\colon I \\rightarrow I<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , a point\n                    <jats:inline-formula>\n                      <jats:tex-math>x \\in I<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    is periodic with period\n                    <jats:inline-formula>\n                      <jats:tex-math>p \\in \\mathbb{N}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    if\n                    <jats:inline-formula>\n                      <jats:tex-math>f^p(x)=x<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    and\n                    <jats:inline-formula>\n                      <jats:tex-math>f^j(x)\\not=x<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    for all\n                    <jats:inline-formula>\n                      <jats:tex-math>0&lt;j&lt;p<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . When\n                    <jats:inline-formula>\n                      <jats:tex-math>f<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    is continuous and\n                    <jats:inline-formula>\n                      <jats:tex-math>I<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    is an interval, a theorem due to Sharkovskii ([1]) states that there is an order in\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathbb{N}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , say\n                    <jats:inline-formula>\n                      <jats:tex-math>\\lhd<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , such that if\n                    <jats:inline-formula>\n                      <jats:tex-math>f<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    has a periodic point of period\n                    <jats:inline-formula>\n                      <jats:tex-math>p<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    and\n                    <jats:inline-formula>\n                      <jats:tex-math>p \\lhd q<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , then\n                    <jats:inline-formula>\n                      <jats:tex-math>f<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    also has a periodic point of period\n                    <jats:inline-formula>\n                      <jats:tex-math>q<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . In this work, we will see how an extension of the order\n                    <jats:inline-formula>\n                      <jats:tex-math>\\lhd<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    to sequences of positive integers yields a Sharkovskii-type result for non-wandering points of\n                    <jats:inline-formula>\n                      <jats:tex-math>f<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    .\n                  <\/jats:p>","DOI":"10.4171\/pm\/1911","type":"journal-article","created":{"date-parts":[[2012,6,27]],"date-time":"2012-06-27T18:12:01Z","timestamp":1340820721000},"page":"159-165","source":"Crossref","is-referenced-by-count":0,"title":["Sharkovskii order for non-wandering points"],"prefix":"10.4171","volume":"69","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6929-6442","authenticated-orcid":false,"given":"Maria Pires","family":"de Carvalho","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/043pwc612","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade do Porto, Portugal"}]},{"given":"Fernando Jorge","family":"Moreira","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/043pwc612","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade do Porto, Portugal"}]}],"member":"2673","container-title":["Portugaliae Mathematica"],"original-title":[],"link":[{"URL":"http:\/\/www.ems-ph.org\/fulltext\/10.4171\/PM\/1911","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T06:53:21Z","timestamp":1775026401000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/pm\/1911"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,27]]},"references-count":0,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.4171\/pm\/1911","relation":{},"ISSN":["0032-5155","1662-2758"],"issn-type":[{"value":"0032-5155","type":"print"},{"value":"1662-2758","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6,27]]}}}