{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,5]],"date-time":"2023-04-05T14:17:10Z","timestamp":1680704230245},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2008,2,1]],"date-time":"2008-02-01T00:00:00Z","timestamp":1201824000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bulletin of the Australian Mathematical Society"],"published-print":{"date-parts":[[2008,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>It is well known that an orientation-preserving homeomorphism of the plane without fixed points has trivial dynamics; that is, its non-wandering set is empty and all the orbits diverge to infinity. However, orbits can diverge to infinity in many different ways (or not) giving rise to <jats:italic>fundamental regions<\/jats:italic> of divergence. Such a map is topologically equivalent to a plane translation if and only if it has only one fundamental region. We consider the conservative, orientation-preserving and fixed point free H\u00e9non map and prove that it has only one fundamental region of divergence. Actually, we prove that there exists an area-preserving homeomorphism of the plane that conjugates this H\u00e9non map to a translation.<\/jats:p>","DOI":"10.1017\/s000497270800004x","type":"journal-article","created":{"date-parts":[[2008,3,12]],"date-time":"2008-03-12T14:19:32Z","timestamp":1205331572000},"page":"37-48","source":"Crossref","is-referenced-by-count":2,"title":["ON THE FUNDAMENTAL REGIONS OF A FIXED POINT FREE CONSERVATIVE H\u00c9NON MAP"],"prefix":"10.1017","volume":"77","author":[{"given":"M\u00c1RIO","family":"BESSA","sequence":"first","affiliation":[]},{"given":"JORGE","family":"ROCHA","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2008,2,1]]},"reference":[{"key":"S000497270800004X_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02993992"},{"key":"S000497270800004X_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01221362"},{"key":"S000497270800004X_ref6","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385700006702"},{"key":"S000497270800004X_ref5","doi-asserted-by":"publisher","DOI":"10.1080\/026811199281930"},{"key":"S000497270800004X_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/0040-9383(94)90016-7"},{"key":"S000497270800004X_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/S0294-1449(16)30307-9"},{"key":"S000497270800004X_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01321309"},{"key":"S000497270800004X_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s10231-004-0142-4"},{"key":"S000497270800004X_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(84)90110-4"}],"container-title":["Bulletin of the Australian Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S000497270800004X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,7]],"date-time":"2019-04-07T19:38:12Z","timestamp":1554665892000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S000497270800004X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,2]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2008,2]]}},"alternative-id":["S000497270800004X"],"URL":"https:\/\/doi.org\/10.1017\/s000497270800004x","relation":{},"ISSN":["0004-9727","1755-1633"],"issn-type":[{"value":"0004-9727","type":"print"},{"value":"1755-1633","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,2]]}}}