{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T14:33:30Z","timestamp":1648737210017},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,4]]},"abstract":"<jats:p> A continuous map f from a metric space X to itself is said to contain a two-sided symbolic dynamical system if there exists an invariant set X<jats:sub>0<\/jats:sub> of f such that the subsystem f|X<jats:sub>0<\/jats:sub> is topologically conjugate to the shift map on a two-sided sequence space of some symbols. In this paper we show that, for any given integer n \u2265 2, there exists a Lipschitz continuous interval map which contains a two-sided symbolic dynamical system of n symbols. Furthermore, we investigate the effect of differentiability and monotonicity assumptions, and prove that neither piecewise monotonic nor piecewise continuously differentiable graph map can contain a two-sided symbolic dynamical system. <\/jats:p>","DOI":"10.1142\/s0218127405012594","type":"journal-article","created":{"date-parts":[[2005,7,5]],"date-time":"2005-07-05T14:52:13Z","timestamp":1120575133000},"page":"1485-1491","source":"Crossref","is-referenced-by-count":0,"title":["WHAT MAPS CAN ADMIT TWO-SIDED SYMBOLIC DYNAMICAL SYSTEMS?"],"prefix":"10.1142","volume":"15","author":[{"given":"JIE-HUA","family":"MAI","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Shantou University, Shantou, Guangdong 515063, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127499001206"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385799126622"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0084762"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1986-0835899-0"},{"key":"rf5","volume-title":"Chaotic Dynamical Systems","author":"Devaney R. L.","year":"1989"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1991-1069687-1"},{"key":"rf7","first-page":"1067","volume":"10","author":"Fu X.-C.","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BF02566944"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.2307\/2318254"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1983-0695270-9"},{"key":"rf11","volume-title":"Topology","author":"Munkres J. R.","year":"1975"},{"key":"rf12","volume-title":"Differentiable Dynamics","author":"Nitecki Z.","year":"1971"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1967-11798-1"},{"key":"rf14","unstructured":"J.\u00a0Xiong, Dynamical Systems, Nankai Series in Pure, Applied Mathematics and Theoretical Physics\u00a04 (World Scientific, Singapore, 1993)\u00a0pp. 273\u2013277."},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(96)00055-7"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127405012594","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T15:03:27Z","timestamp":1565190207000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127405012594"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,4]]},"references-count":15,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,4]]}},"alternative-id":["10.1142\/S0218127405012594"],"URL":"https:\/\/doi.org\/10.1142\/s0218127405012594","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,4]]}}}