{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,28]],"date-time":"2023-10-28T16:46:56Z","timestamp":1698511616383},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,4,9]],"date-time":"2014-04-09T00:00:00Z","timestamp":1397001600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Proc. Camb. Phil. Soc."],"published-print":{"date-parts":[[2014,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We construct a Hamiltonian suspension for a given symplectomorphism which is the perturbation of a Poincar\u00e9 map. This is especially useful for the conversion of perturbative results between symplectomorphisms and Hamiltonian flows in any dimension <jats:italic>2d<\/jats:italic>. As an application, using known properties of area-preserving maps, we prove that for any Hamiltonian defined on a symplectic 4-manifold <jats:italic>M<\/jats:italic> and any point <jats:italic>p<\/jats:italic> \u2208 <jats:italic>M<\/jats:italic>, there exists a <jats:italic>C<\/jats:italic><jats:sup>2<\/jats:sup>-close Hamiltonian whose regular energy surface through <jats:italic>p<\/jats:italic> is either Anosov or contains a homoclinic tangency.<\/jats:p>","DOI":"10.1017\/s0305004114000140","type":"journal-article","created":{"date-parts":[[2014,4,9]],"date-time":"2014-04-09T08:53:56Z","timestamp":1397033636000},"page":"101-112","source":"Crossref","is-referenced-by-count":2,"title":["Hamiltonian suspension of perturbed Poincar\u00e9 sections and an application"],"prefix":"10.1017","volume":"157","author":[{"given":"M\u00c1RIO","family":"BESSA","sequence":"first","affiliation":[]},{"given":"JO\u00c1O LOPES","family":"DIAS","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,4,9]]},"reference":[{"key":"S0305004114000140_ref17","doi-asserted-by":"publisher","DOI":"10.1007\/BF01431464"},{"key":"S0305004114000140_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(98)00279-6"},{"key":"S0305004114000140_ref10","doi-asserted-by":"publisher","DOI":"10.1134\/S156035471002005X"},{"key":"S0305004114000140_ref12","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2004.160.375"},{"key":"S0305004114000140_ref9","doi-asserted-by":"publisher","DOI":"10.1080\/14689367.2012.655710"},{"key":"S0305004114000140_ref13","doi-asserted-by":"publisher","DOI":"10.2307\/2374000"},{"key":"S0305004114000140_ref16","doi-asserted-by":"publisher","DOI":"10.2307\/121127"},{"key":"S0305004114000140_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/S0294-1449(03)00016-7"},{"key":"S0305004114000140_ref18","unstructured":"T. Vivier . Robustly transitive 3-dimensional regular energy surface are Anosov. Institut de Math\u00e9matiques de Bourgogne, Dijon, Preprint 412 (2005). http:\/\/math.u-bourgogne.fr\/topo\/prepub\/pre05.html."},{"key":"S0305004114000140_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2009.07.020"},{"key":"S0305004114000140_ref11","doi-asserted-by":"publisher","DOI":"10.5802\/afst.885"},{"key":"S0305004114000140_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-008-0500-y"},{"key":"S0305004114000140_ref14","first-page":"339","article-title":"A global view of dynamics and a conjecture on the denseness of finitude of attractors.","volume":"261","author":"Palis","year":"2000","journal-title":"Ast\u00e9risque"},{"key":"S0305004114000140_ref2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-08-09578-6"},{"key":"S0305004114000140_ref15","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/21\/4\/T01"},{"key":"S0305004114000140_ref8","doi-asserted-by":"publisher","DOI":"10.1080\/026811199281930"},{"key":"S0305004114000140_ref7","first-page":"201","article-title":"Une d\u00e9monstration directe de l'\u00e9quivalence des th\u00e9or\u00e8mes de tores invariants pour diff\u00e9omorphismes et champs de vecteurs.","volume":"295","author":"Douady","year":"1982","journal-title":"C. 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