{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T18:23:56Z","timestamp":1775845436170,"version":"3.50.1"},"reference-count":33,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2008,10,1]],"date-time":"2008-10-01T00:00:00Z","timestamp":1222819200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ergod. Th. Dynam. Sys."],"published-print":{"date-parts":[[2008,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In Bunimovich and Del Magno [Semi-focusing billiards: hyperbolicity. <jats:italic>Comm. Math. Phys.<\/jats:italic><jats:bold>262<\/jats:bold> (2006), 17\u201332], we proved that billiards in certain three-dimensional convex domains are hyperbolic. In this paper, we continue the study of these systems, and prove that they enjoy the Bernoulli property. This result answers affirmatively a long-standing question on the existence of ergodic billiards in convex domains in dimensions greater than two. Besides, it shows that the chaotic components of the first rigorously investigated three-dimensional billiards with mixed phase space (mushroom billiards), introduced in Bunimovich and Del Magno, are in fact Bernoulli.<\/jats:p>","DOI":"10.1017\/s0143385707000909","type":"journal-article","created":{"date-parts":[[2008,7,29]],"date-time":"2008-07-29T05:49:18Z","timestamp":1217310558000},"page":"1377-1417","source":"Crossref","is-referenced-by-count":6,"title":["Semi-focusing billiards: ergodicity"],"prefix":"10.1017","volume":"28","author":[{"given":"LEONID A.","family":"BUNIMOVICH","sequence":"first","affiliation":[]},{"given":"GIANLUIGI","family":"DEL MAGNO","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2008,10,1]]},"reference":[{"key":"S0143385707000909_ref33","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-007-0226-2"},{"key":"S0143385707000909_ref25","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385798100354"},{"key":"S0143385707000909_ref23","doi-asserted-by":"publisher","DOI":"10.5802\/afst.779"},{"key":"S0143385707000909_ref22","doi-asserted-by":"publisher","DOI":"10.1007\/BF01218478"},{"key":"S0143385707000909_ref7","first-page":"119","article-title":"Geometry of multi-dimensional dispersing billiards","volume":"286","author":"B\u00e1lint","year":"2003","journal-title":"Ast\u00e9risque"},{"key":"S0143385707000909_ref18","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385700008142"},{"key":"S0143385707000909_ref17","doi-asserted-by":"publisher","DOI":"10.1007\/BF02101504"},{"key":"S0143385707000909_ref30","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385700002807"},{"key":"S0143385707000909_ref31","doi-asserted-by":"publisher","DOI":"10.1007\/BF01205934"},{"key":"S0143385707000909_ref14","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385700008695"},{"key":"S0143385707000909_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01197884"},{"key":"S0143385707000909_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s00023-002-8624-7"},{"key":"S0143385707000909_ref1","first-page":"73","article-title":"The ergodic properties of certain billiards","volume":"8","author":"Bunimovich","year":"1974","journal-title":"Funkt. 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