{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T05:16:54Z","timestamp":1772774214386,"version":"3.50.1"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12362002"],"award-info":[{"award-number":["12362002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12172306"],"award-info":[{"award-number":["12172306"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12302015"],"award-info":[{"award-number":["12302015"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2026,4]]},"abstract":"<jats:p>The breathing circular billiard models the free motion of a point particle within a circular enclosure whose boundary undergoes periodic motion. It is assumed that the particle experiences elastic collisions with the boundary. Previous studies have demonstrated that when the boundary motion is sufficiently regular (specifically, [Formula: see text] smooth), the energy of the particle remains bounded due to the existence of invariant curves in the phase space. In this work, under the assumption that the motion of the boundary is [Formula: see text], we prove that the set of initial conditions that give rise to escaping orbits has Lebesgue measure zero, imparting orbit stability to the breathing circular billiard.<\/jats:p>","DOI":"10.1142\/s0218127426500574","type":"journal-article","created":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T08:03:48Z","timestamp":1767600228000},"source":"Crossref","is-referenced-by-count":0,"title":["Recurrent Motions in the Breathing Circle Billiard"],"prefix":"10.1142","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5786-6313","authenticated-orcid":false,"given":"Denghui","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Suzhou University of Technology, Changshu 215500, Jiangsu, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1332-7665","authenticated-orcid":false,"given":"Xiaoming","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 610032, Sichuan, P. R. China"}]},{"given":"Jianhua","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 610032, Sichuan, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9811-4617","authenticated-orcid":false,"given":"Celso","family":"Grebogi","sequence":"additional","affiliation":[{"name":"Institute for Complex Systems and Mathematical Biology, King\u2019s College, University of Aberdeen, Aberdeen AB24 3FX, UK"}]}],"member":"219","published-online":{"date-parts":[[2026,1,3]]},"reference":[{"key":"S0218127426500574BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2063-1"},{"key":"S0218127426500574BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s00023-021-01090-9"},{"key":"S0218127426500574BIB003","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevC.52.2475"},{"key":"S0218127426500574BIB004","first-page":"1","volume":"20","author":"Cao Z.","year":"2021","journal-title":"Qual. Theory Differ. Equ."},{"key":"S0218127426500574BIB005","doi-asserted-by":"publisher","DOI":"10.1080\/1468936021000041654"},{"key":"S0218127426500574BIB006","volume-title":"Piecewise-Smooth Dynamical Systems: Theory and Applications","author":"di Bernardo M.","year":"2007"},{"key":"S0218127426500574BIB007","series-title":"Lecture Notes for a Course in Murcia","volume-title":"Lectures on Bouncing Balls","author":"Dolgopyat D.","year":"2013"},{"key":"S0218127426500574BIB008","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/12\/5\/310"},{"key":"S0218127426500574BIB009","doi-asserted-by":"publisher","DOI":"10.1017\/etds.2018.77"},{"key":"S0218127426500574BIB010","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385700006192"},{"key":"S0218127426500574BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/0022-460X(91)90592-8"},{"key":"S0218127426500574BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/s00023-022-01217-6"},{"key":"S0218127426500574BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/s12346-021-00545-y"},{"key":"S0218127426500574BIB014","doi-asserted-by":"publisher","DOI":"10.1063\/1.3695379"},{"key":"S0218127426500574BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/0022-460X(92)90480-L"},{"key":"S0218127426500574BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2021.111643"},{"key":"S0218127426500574BIB017","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/11\/6\/003"},{"key":"S0218127426500574BIB018","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/13\/4\/308"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127426500574","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T04:09:38Z","timestamp":1772770178000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218127426500574"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,3]]},"references-count":18,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2026,4]]}},"alternative-id":["10.1142\/S0218127426500574"],"URL":"https:\/\/doi.org\/10.1142\/s0218127426500574","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,3]]},"article-number":"2650057"}}