{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T14:57:50Z","timestamp":1776265070332,"version":"3.50.1"},"reference-count":14,"publisher":"American Mathematical Society (AMS)","issue":"2","license":[{"start":{"date-parts":[[2009,8,20]],"date-time":"2009-08-20T00:00:00Z","timestamp":1250726400000},"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 consider\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                    -Hamiltonian functions on compact\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"4\">\n                        <mml:semantics>\n                          <mml:mn>4<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">4<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -dimensional symplectic manifolds to study the elliptic dynamics of the Hamiltonian flow, namely the so-called Newhouse dichotomy. We show that for any open set\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper U\">\n                        <mml:semantics>\n                          <mml:mi>U<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">U<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    intersecting a far from Anosov regular energy surface, there is a nearby Hamiltonian having an elliptic closed orbit through\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper U\">\n                        <mml:semantics>\n                          <mml:mi>U<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">U<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Moreover, this implies that, for far from Anosov regular energy surfaces of a\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                    -generic Hamiltonian, the elliptic closed orbits are generic.\n                  <\/p>","DOI":"10.1090\/s0002-9939-08-09578-6","type":"journal-article","created":{"date-parts":[[2008,10,23]],"date-time":"2008-10-23T13:23:15Z","timestamp":1224768195000},"page":"585-592","source":"Crossref","is-referenced-by-count":8,"special_numbering":"596","title":["Hamiltonian elliptic dynamics on symplectic 4-manifolds"],"prefix":"10.1090","volume":"137","author":[{"given":"M\u00e1rio","family":"Bessa","sequence":"first","affiliation":[]},{"given":"Jo\u00e3o","family":"Dias","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2008,8,20]]},"reference":[{"issue":"5","key":"1","doi-asserted-by":"publisher","first-page":"1399","DOI":"10.1017\/S014338570700017X","article-title":"A pasting lemma and some applications for conservative systems","volume":"27","author":"Arbieto, Alexander","year":"2007","journal-title":"Ergodic Theory Dynam. 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Vivier, Robustly transitive 3-dimensional regular energy surfaces are Anosov, Institut de Math\u00e9matiques de Bourgogne, Dijon, Preprint 412 (2005). \\url{http:\/\/math.u-bourgogne.fr\/topo\/prepub\/pre05.html}"}],"container-title":["Proceedings of the American Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/proc\/2009-137-02\/S0002-9939-08-09578-6\/S0002-9939-08-09578-6.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/proc\/2009-137-02\/S0002-9939-08-09578-6\/S0002-9939-08-09578-6.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T14:00:36Z","timestamp":1776261636000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/proc\/2009-137-02\/S0002-9939-08-09578-6\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,8,20]]},"references-count":14,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2009,2]]}},"alternative-id":["S0002-9939-08-09578-6"],"URL":"https:\/\/doi.org\/10.1090\/s0002-9939-08-09578-6","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6826","0002-9939"],"issn-type":[{"value":"1088-6826","type":"electronic"},{"value":"0002-9939","type":"print"}],"subject":[],"published":{"date-parts":[[2008,8,20]]}}}