{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T00:34:20Z","timestamp":1773707660372,"version":"3.50.1"},"reference-count":30,"publisher":"American Mathematical Society (AMS)","license":[{"start":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T00:00:00Z","timestamp":1784160000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/05069\/2020"],"award-info":[{"award-number":["UIDB\/05069\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proc. Amer. Math. Soc."],"abstract":"<p>\n                    We consider a semi-Riemannian metric whose associated geodesic flow either contains a non-hyperbolic periodic orbit or has infinitely many hyperbolic periodic orbits. Under some conditions, we show that the metric can be\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper C squared\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>C<\/mml:mi>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">C^2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -perturbed such that the geodesic flow exhibits positive topological entropy, there are infinitely many non-lightlike closed geodesics, and their number grows exponentially with respect to the length.\n                  <\/p>","DOI":"10.1090\/proc\/17337","type":"journal-article","created":{"date-parts":[[2025,7,16]],"date-time":"2025-07-16T14:42:03Z","timestamp":1752676923000},"source":"Crossref","is-referenced-by-count":0,"title":["Positive topological entropy for semi-Riemannian geodesic flows"],"prefix":"10.1090","author":[{"given":"M\u00e1rio","family":"Bessa","sequence":"first","affiliation":[]},{"given":"Jo\u00e3o","family":"Lopes Dias","sequence":"additional","affiliation":[]},{"given":"Pedro","family":"Matias","sequence":"additional","affiliation":[]},{"given":"Maria","family":"Torres","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2025,7,16]]},"reference":[{"key":"1","isbn-type":"print","volume-title":"Foundations of mechanics","author":"Abraham, Ralph","year":"1978","ISBN":"https:\/\/id.crossref.org\/isbn\/080530102X"},{"issue":"2","key":"2","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1017\/S0305004100067347","article-title":"Geodesic completeness and stability","volume":"102","author":"Beem, John K.","year":"1987","journal-title":"Math. 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