{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T04:27:07Z","timestamp":1774326427633,"version":"3.50.1"},"reference-count":33,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12371167"],"award-info":[{"award-number":["12371167"]}],"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":["12001148"],"award-info":[{"award-number":["12001148"]}],"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":["12371167"],"award-info":[{"award-number":["12371167"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Shandong Provincial Natural Science Foundation","doi-asserted-by":"crossref","award":["ZR2023QA108"],"award-info":[{"award-number":["ZR2023QA108"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271380"],"award-info":[{"award-number":["12271380"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key R&D Program of China","doi-asserted-by":"crossref","award":["2021YFA1001600"],"award-info":[{"award-number":["2021YFA1001600"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12371189"],"award-info":[{"award-number":["12371189"]}],"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":["12071254"],"award-info":[{"award-number":["12071254"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2024,6,30]]},"DOI":"10.1137\/22m1512958","type":"journal-article","created":{"date-parts":[[2024,5,24]],"date-time":"2024-05-24T12:27:42Z","timestamp":1716553662000},"page":"3605-3645","source":"Crossref","is-referenced-by-count":2,"title":["On Linear Stability of KAM Tori via the Craig\u2013Wayne\u2013Bourgain Method"],"prefix":"10.1137","volume":"56","author":[{"given":"Xiaolong","family":"He","sequence":"first","affiliation":[{"name":"School of Mathematics, Hangzhou Normal University, Hangzhou, China."}]},{"given":"Jia","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Mathematics, Shandong University, Jinan, China."}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7383-8491","authenticated-orcid":true,"given":"Yunfeng","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Mathematics, Sichuan University, Chengdu, China."}]},{"given":"Xiaoping","family":"Yuan","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Fudan University, Shanghai, China."}]}],"member":"351","published-online":{"date-parts":[[2024,5,24]]},"reference":[{"key":"ref1","first-page":"21","volume":"25","author":"Arnol\u2019d V. I.","year":"1961","journal-title":"Izv. Akad. Nauk SSSR Ser. Mat."},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s40574-016-0067-z"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.4171\/jems\/361"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.4171\/211"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-014-2128-4"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61900-7"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.4310\/MRL.1997.v4.n4.a1"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.2307\/121001"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1515\/9781400837144"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392795"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.4171\/jems\/102"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/7699"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160461102"},{"key":"ref14","first-page":"115","volume":"15","author":"Eliasson L. H.","year":"1988","journal-title":"Ann. Sc. Norm. Super. Pisa Cl. Sci. (4)"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1007\/s00039-016-0390-7"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2010.172.371"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2011.01.013"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-08054-2"},{"key":"ref20","first-page":"527","volume":"98","author":"Kolmogorov A. N.","year":"1954","journal-title":"Dokl. Akad. Nauk SSSR (N.S.)"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0092243"},{"key":"ref22","first-page":"546","volume":"181","author":"Mel\u2019nikov V. K.","year":"1968","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"ref23","first-page":"1","volume":"1962","author":"Moser J.","year":"1962","journal-title":"Nachr. Akad. Wiss. G\u00f6ttingen Math.-Phys. Kl. II"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1007\/BF01221590"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/069\/1858551"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2014.12.004"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-012-1483-2"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2019.05.039"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1215\/00127094-3167597"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1142\/9789811208379_0003"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-020-03798-x"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1998.3515"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1360\/N012016-00154"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.21931"}],"container-title":["SIAM Journal on Mathematical Analysis"],"original-title":[],"language":"en","deposited":{"date-parts":[[2024,6,28]],"date-time":"2024-06-28T17:32:50Z","timestamp":1719595970000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/22M1512958"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,24]]},"references-count":33,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,6,30]]}},"alternative-id":["10.1137\/22M1512958"],"URL":"https:\/\/doi.org\/10.1137\/22m1512958","relation":{},"ISSN":["0036-1410","1095-7154"],"issn-type":[{"value":"0036-1410","type":"print"},{"value":"1095-7154","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,24]]}}}