{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T15:35:46Z","timestamp":1759073746176},"reference-count":34,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2017,6,15]]},"abstract":"<jats:p> In this paper, the chaotic dynamics of composition operators on the space of real-valued continuous functions is investigated. It is proved that the hypercyclicity, topologically mixing property, Devaney chaos, frequent hypercyclicity and the specification property of the composition operator are equivalent to each other and are stronger than dense distributional chaos. Moreover, the composition operator [Formula: see text] exhibits dense Li\u2013Yorke chaos if and only if it is densely distributionally chaotic, if and only if the symbol [Formula: see text] admits no fixed points. Finally, the long-time behaviors of the composition operator with affine symbol are classified in detail. <\/jats:p>","DOI":"10.1142\/s0218127417500845","type":"journal-article","created":{"date-parts":[[2017,7,3]],"date-time":"2017-07-03T23:24:48Z","timestamp":1499124288000},"page":"1750084","source":"Crossref","is-referenced-by-count":3,"title":["Chaotic Dynamics of Composition Operators on the Space of Continuous Functions"],"prefix":"10.1142","volume":"27","author":[{"given":"Zongbin","family":"Yin","sequence":"first","affiliation":[{"name":"School of Mathematics, Sun Yat-sen University, Guangzhou 510275, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2017,7,3]]},"reference":[{"key":"S0218127417500845BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2015.12.004"},{"key":"S0218127417500845BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2004.02.012"},{"key":"S0218127417500845BIB003","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-06-04019-0"},{"key":"S0218127417500845BIB004","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511581113"},{"key":"S0218127417500845BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2010.06.011"},{"key":"S0218127417500845BIB006","doi-asserted-by":"publisher","DOI":"10.1080\/17476939508814804"},{"key":"S0218127417500845BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2013.06.019"},{"key":"S0218127417500845BIB008","doi-asserted-by":"publisher","DOI":"10.1017\/etds.2014.20"},{"key":"S0218127417500845BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s13398-012-0088-0"},{"key":"S0218127417500845BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/BF02401754"},{"key":"S0218127417500845BIB011","first-page":"473","volume":"189","author":"Birkhoff G. D.","year":"1929","journal-title":"C. R. Acad. Sci. Paris"},{"key":"S0218127417500845BIB012","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004112000266"},{"key":"S0218127417500845BIB014","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/051.2\/1077418"},{"key":"S0218127417500845BIB015","first-page":"x+105","volume":"125","author":"Bourdon P.","year":"1997","journal-title":"Mem. Amer. Math. Soc."},{"key":"S0218127417500845BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/s11785-013-0348-9"},{"key":"S0218127417500845BIB017","first-page":"369","volume":"61","author":"De la Rosa M.","year":"2009","journal-title":"J. Operat. Th."},{"key":"S0218127417500845BIB018","volume-title":"An Introduction to Chaotic Dynamical Systems","author":"Devaney R. L.","year":"1989"},{"key":"S0218127417500845BIB019","first-page":"x+81","volume":"167","author":"Gallardo-Guti\u00e9rrez E. A.","year":"2004","journal-title":"Mem. Amer. Math. Soc."},{"key":"S0218127417500845BIB020","doi-asserted-by":"publisher","DOI":"10.1007\/s11854-009-0013-4"},{"key":"S0218127417500845BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-2170-1"},{"key":"S0218127417500845BIB022","doi-asserted-by":"publisher","DOI":"10.15352\/bjma\/09-2-9"},{"key":"S0218127417500845BIB023","volume-title":"Lectures on Ergodic Theory","author":"Halmos P. R.","year":"1965"},{"key":"S0218127417500845BIB024","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2013.12.004"},{"key":"S0218127417500845BIB025","doi-asserted-by":"publisher","DOI":"10.1007\/BF00532810"},{"key":"S0218127417500845BIB026","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1975.11994008"},{"key":"S0218127417500845BIB027","doi-asserted-by":"publisher","DOI":"10.1007\/s00209-012-1087-8"},{"key":"S0218127417500845BIB028","doi-asserted-by":"publisher","DOI":"10.1007\/BF01562537"},{"key":"S0218127417500845BIB029","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-09-04810-7"},{"key":"S0218127417500845BIB030","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511608728"},{"key":"S0218127417500845BIB031","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1994-1227094-X"},{"key":"S0218127417500845BIB033","volume-title":"Composition Operators on Function Spaces","author":"Singh R. K.","year":"1993"},{"key":"S0218127417500845BIB034","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/27\/2\/271"},{"key":"S0218127417500845BIB035","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127415501783"},{"key":"S0218127417500845BIB036","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-07-08833-8"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127417500845","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T15:45:02Z","timestamp":1565106302000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127417500845"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,15]]},"references-count":34,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2017,7,3]]},"published-print":{"date-parts":[[2017,6,15]]}},"alternative-id":["10.1142\/S0218127417500845"],"URL":"https:\/\/doi.org\/10.1142\/s0218127417500845","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,6,15]]}}}