{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T13:33:58Z","timestamp":1760621638629},"reference-count":18,"publisher":"World Scientific Pub Co Pte Lt","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2001,10]]},"abstract":"<jats:p> Riddling occurs in dissipative dynamical systems with more than one attractor, when the basin of one attractor is punctured with holes belonging to the basins of the other attractors. The basin of a chaotic attractor is riddled if (i) it has a positive Lebesgue measure; (ii) in the vicinity of every point belonging to the basin of the attractor, there is a positive Lebesgue measure set of points that asymptote to another attractor. We investigate the presence of riddled basins in a two-dimensional noninvertible map with a symmetry-breaking term. In the symmetric case the onset of riddling is characterized by an unstable\u2013unstable pair bifurcation, which also leads to unstable dimension variability in the invariant chaotic set. The nonsymmetric case exhibits a chaotic attractor, but a riddled basin occurs only at the bifurcation point, since after that the attractor becomes a chaotic saddle. We analyze the presence of unstable dimension variability in the symmetric case by computing the finite-time transverse Lyapunov exponents. We point out some consequences of those facts to the synchronization properties of coupled chaotic systems. <\/jats:p>","DOI":"10.1142\/s0218127401003772","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:02:01Z","timestamp":1027767721000},"page":"2689-2698","source":"Crossref","is-referenced-by-count":13,"title":["RIDDLED BASINS AND UNSTABLE DIMENSION VARIABILITY IN CHAOTIC SYSTEMS WITH AND WITHOUT SYMMETRY"],"prefix":"10.1142","volume":"11","author":[{"given":"RICARDO L.","family":"VIANA","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Universidade Federal do Paran\u00e1, Caixa Postal 19081, 81531-990, Curitiba, PR, Brazil"}]},{"given":"CELSO","family":"GREBOGI","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica, Universidade de S\u00e3o Paulo, Caixa Postal 66318, 05315-970, S\u00e3o Paulo, SP, Brazil"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127492000446"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.85.2490"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.50.935"},{"key":"p_5","first-page":"125","volume":"17","author":"Grebogi C.","year":"1985","journal-title":"Physica"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1017\/S014338570000300X"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(85)90220-8"},{"key":"p_9","doi-asserted-by":"crossref","first-page":"1874","DOI":"10.1103\/PhysRevB.50.1874","volume":"50","author":"Heagy J. F.","year":"1994","journal-title":"Phys. Rev."},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1007\/BF01941800"},{"key":"p_11","first-page":"81","volume":"109","author":"Kostelich E. J.","year":"1997","journal-title":"Physica"},{"key":"p_12","first-page":"1371","volume":"53","author":"Lai Y.-C.","year":"1996","journal-title":"Phys. Rev."},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.77.55"},{"key":"p_14","first-page":"2907","volume":"59","author":"Lai Y.-C.","year":"1999","journal-title":"Phys. Rev."},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.82.4803"},{"key":"p_16","first-page":"5445","volume":"60","author":"Lai Y.-C.","year":"1999","journal-title":"Phys. Rev."},{"key":"p_17","author":"Lai Y.-C.","year":"2000","journal-title":"Phys. Rev. E62, R4505-R4508."},{"key":"p_18","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127400000487"},{"key":"p_19","doi-asserted-by":"publisher","DOI":"10.1063\/1.166278"},{"key":"p_20","first-page":"462","volume":"62","author":"Viana R. L.","year":"2000","journal-title":"Phys. Rev."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127401003772","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T15:06:16Z","timestamp":1565190376000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127401003772"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,10]]},"references-count":18,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2001,10]]}},"alternative-id":["10.1142\/S0218127401003772"],"URL":"https:\/\/doi.org\/10.1142\/s0218127401003772","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,10]]}}}