{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T22:37:26Z","timestamp":1773182246622,"version":"3.50.1"},"reference-count":21,"publisher":"American Mathematical Society (AMS)","issue":"4","license":[{"start":{"date-parts":[[2022,2,12]],"date-time":"2022-02-12T00:00:00Z","timestamp":1644624000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proc. Amer. Math. Soc."],"abstract":"<p>\n                    We prove that given a non-wandering point of a Sobolev-\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"left-parenthesis 1 comma p right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">(1,p)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    homeomorphism we can create closed trajectories by making arbitrarily small perturbations. As an application, in the planar case, we obtain that generically the closed trajectories are dense in the non-wandering set.\n                  <\/p>","DOI":"10.1090\/proc\/15352","type":"journal-article","created":{"date-parts":[[2021,2,12]],"date-time":"2021-02-12T08:59:35Z","timestamp":1613120375000},"page":"1687-1696","source":"Crossref","is-referenced-by-count":1,"special_numbering":"742","title":["The closing lemma and the planar general density theorem for Sobolev maps"],"prefix":"10.1090","volume":"149","author":[{"given":"Assis","family":"Azevedo","sequence":"first","affiliation":[]},{"given":"Davide","family":"Azevedo","sequence":"additional","affiliation":[]},{"given":"M\u00e1rio","family":"Bessa","sequence":"additional","affiliation":[]},{"given":"Maria","family":"Torres","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2021,2,12]]},"reference":[{"issue":"6","key":"1","doi-asserted-by":"publisher","first-page":"697","DOI":"10.1134\/S1560354713060099","article-title":"\ud835\udc36\u00b9-generic billiard tables have a dense set of periodic points","volume":"18","author":"Arnaud, Marie-Claude","year":"2013","journal-title":"Regul. 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