{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T02:39:41Z","timestamp":1648867181453},"reference-count":19,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2003,3]]},"abstract":"<jats:p> We investigate the structure of dynamical correlations on reconstructed attractors which were obtained by time-delay embedding of periodic, quasi-periodic and chaotic time series. Within the specific sampling of the invariant density by a finite number of vectors which results from embedding, we identify two separate levels of sampling, corresponding to two different types of dynamical correlations, each of which produces characteristic artifacts in correlation dimension estimation: the well-known trajectory bias and a characteristic oscillation due to periodic sampling. For the second artifact we propose random sampling as a new correction method which is shown to provide improved sampling and to reduce dynamical correlations more efficiently than it has been possible by the standard Theiler correction. For accurate numerical analysis of correlation dimension in a bootstrap framework both corrections should be combined. For tori and the Lorenz attractor we also show how to construct time-delay embeddings which are completely free of any dynamical correlations. <\/jats:p>","DOI":"10.1142\/s0218127403006881","type":"journal-article","created":{"date-parts":[[2003,4,8]],"date-time":"2003-04-08T07:12:24Z","timestamp":1049785944000},"page":"723-732","source":"Crossref","is-referenced-by-count":2,"title":["DYNAMICAL CORRELATIONS ON RECONSTRUCTED INVARIANT  DENSITIES AND THEIR EFFECT ON CORRELATION DIMENSION ESTIMATION"],"prefix":"10.1142","volume":"13","author":[{"given":"ANDREAS","family":"GALKA","sequence":"first","affiliation":[{"name":"Institute of Experimental and Applied Physics, University of Kiel, 24098 Kiel, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"GERD","family":"PFISTER","sequence":"additional","affiliation":[{"name":"Institute of Experimental and Applied Physics, University of Kiel, 24098 Kiel, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.45.7073"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.1994.0095"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01010905"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.53.5831"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(98)00168-7"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/9789812813237"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(90)90577-B"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(83)90298-1"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127491000403"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.50.1770"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(94)90008-6"},{"key":"rf12","volume-title":"Nonlinear Time Series Analysis","author":"Kantz H.","year":"1997"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02183688"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(92)90100-2"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0091924"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.34.2427"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(88)91016-X"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.7.001055"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.41.3038"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127403006881","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:14:17Z","timestamp":1565122457000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127403006881"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,3]]},"references-count":19,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,3]]}},"alternative-id":["10.1142\/S0218127403006881"],"URL":"https:\/\/doi.org\/10.1142\/s0218127403006881","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,3]]}}}