{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T20:52:45Z","timestamp":1648932765261},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2013,8]]},"abstract":"<jats:p> This paper provides a topological dynamics perspective on the full bifurcation unfolding in unimodal mappings. We present a bundle structure, visualized as a bundle plot, to show the evolution of symbolic space as we vary a system parameter. The bundle plot can be viewed as a limit process of an assignment plot, which are line assignments between points from two dynamical systems. Such line assignments are determined by a commuter, which is a coordinates transformation function that satisfies a commuting relationship but not necessarily a homeomorphism. The bundle structure is studied by understanding the implication of the system's qualitative changes. In addition, the case of the bundle plot with higher dimensional parameter variation is also considered. A main concern in the bundle plot is a special structure, called \"joint\", which determines a critical value of the parameter where the kneading sequence becomes periodic. <\/jats:p>","DOI":"10.1142\/s0218127413300280","type":"journal-article","created":{"date-parts":[[2013,9,18]],"date-time":"2013-09-18T07:08:56Z","timestamp":1379488136000},"page":"1330028","source":"Crossref","is-referenced-by-count":0,"title":["THE BUNDLE PLOT: EVOLUTION OF SYMBOLIC SPACE UNDER THE SYSTEM PARAMETER CHANGES"],"prefix":"10.1142","volume":"23","author":[{"given":"JIONGXUAN","family":"ZHENG","sequence":"first","affiliation":[{"name":"Mathematics and Computer Science, Clarkson University, Potsdam, NY 13699, United States"}]},{"given":"JOSEPH D.","family":"SKUFCA","sequence":"additional","affiliation":[{"name":"Mathematics and Computer Science, Clarkson University, Potsdam, NY 13699, United States"}]},{"given":"ERIK M.","family":"BOLLT","sequence":"additional","affiliation":[{"name":"Mathematics and Computer Science, Clarkson University, Potsdam, NY 13699, United States"}]}],"member":"219","published-online":{"date-parts":[[2013,9,18]]},"reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2009.12.007"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0082847"},{"key":"p_6","doi-asserted-by":"crossref","first-page":"215","DOI":"10.4064\/fm-132-3-215-226","volume":"132","author":"Misiurewicz M.","year":"1989","journal-title":"Fund. Math."},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1007\/BF02742713"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1063\/1.2837397"},{"key":"p_12","first-page":"363","volume":"18","author":"Zheng J.","year":"2011","journal-title":"DCDIS Ser. A: Math. Anal."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127413300280","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:51:03Z","timestamp":1565117463000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127413300280"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8]]},"references-count":6,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2013,9,17]]},"published-print":{"date-parts":[[2013,8]]}},"alternative-id":["10.1142\/S0218127413300280"],"URL":"https:\/\/doi.org\/10.1142\/s0218127413300280","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,8]]}}}