{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:52:25Z","timestamp":1760784745716},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2019,11,12]],"date-time":"2019-11-12T00:00:00Z","timestamp":1573516800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proceedings of the Edinburgh Mathematical Society"],"published-print":{"date-parts":[[2020,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We begin by defining a homoclinic class for homeomorphisms. Then we prove that if a topological homoclinic class <jats:italic>\u039b<\/jats:italic> associated with an area-preserving homeomorphism <jats:italic>f<\/jats:italic> on a surface <jats:italic>M<\/jats:italic> is topologically hyperbolic (i.e. has the shadowing and expansiveness properties), then <jats:italic>\u039b<\/jats:italic> = <jats:italic>M<\/jats:italic> and <jats:italic>f<\/jats:italic> is an Anosov homeomorphism.<\/jats:p>","DOI":"10.1017\/s0013091519000282","type":"journal-article","created":{"date-parts":[[2019,11,12]],"date-time":"2019-11-12T10:48:32Z","timestamp":1573555712000},"page":"217-228","source":"Crossref","is-referenced-by-count":2,"title":["There are no proper topological hyperbolic homoclinic classes for area-preserving maps"],"prefix":"10.1017","volume":"63","author":[{"given":"M\u00e1rio","family":"Bessa","sequence":"first","affiliation":[]},{"given":"Maria Joana","family":"Torres","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2019,11,12]]},"reference":[{"key":"S0013091519000282_ref11","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1967-11798-1"},{"key":"S0013091519000282_ref10","doi-asserted-by":"publisher","DOI":"10.1515\/9781400874842-006"},{"key":"S0013091519000282_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-1947-5"},{"key":"S0013091519000282_ref8","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/014\/0267603"},{"key":"S0013091519000282_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5703-5"},{"key":"S0013091519000282_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-1221-5_4"},{"key":"S0013091519000282_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BF02585472"},{"key":"S0013091519000282_ref1","first-page":"783","article-title":"Dynamics of topologically generic homeomorphisms","volume":"164","author":"Akin","year":"2003","journal-title":"Mem. Am. Math. Soc."},{"key":"S0013091519000282_ref5","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1972-0295388-6"},{"key":"S0013091519000282_ref3","first-page":"117","article-title":"Expansive homeomorphisms of compact surfaces are pseudo-Anosov","volume":"27","author":"Hiraide","year":"1990","journal-title":"Osaka J. Math."},{"key":"S0013091519000282_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/S0924-6509(08)70161-2"}],"container-title":["Proceedings of the Edinburgh Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0013091519000282","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,11]],"date-time":"2020-05-11T11:37:39Z","timestamp":1589197059000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0013091519000282\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,12]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,2]]}},"alternative-id":["S0013091519000282"],"URL":"https:\/\/doi.org\/10.1017\/s0013091519000282","relation":{},"ISSN":["0013-0915","1464-3839"],"issn-type":[{"value":"0013-0915","type":"print"},{"value":"1464-3839","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,12]]}}}