{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:31:34Z","timestamp":1787232694543,"version":"build-2736575974"},"reference-count":27,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>We propose a general algorithm for computer assisted verification of uniform hyperbolicity for maps which exhibit a robust attractor. The method has been successfully applied to a Poincar\u00e9 map for a system of coupled nonautonomous van der Pol oscillators. The model equation has been proposed by Kuznetsov [Phys. Rev. Lett., 95 (2005), paper 144101], and the attractor seems to be of the Smale\u2013Williams type.<\/jats:p>","DOI":"10.1137\/100795176","type":"journal-article","created":{"date-parts":[[2010,11,9]],"date-time":"2010-11-09T18:51:20Z","timestamp":1289328680000},"page":"1263-1283","source":"Crossref","is-referenced-by-count":42,"title":["Uniformly Hyperbolic Attractor of the Smale\u2013Williams Type for a Poincar\u00e9 Map in the Kuznetsov System"],"prefix":"10.1137","volume":"9","author":[{"given":"Daniel","family":"Wilczak","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,11,9]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1080\/10586458.2007.10128992"},{"key":"R2","unstructured":"CAPD\u2014Computer assisted proofs in dynamics\n                      , a software package for rigorous numerics, available online at http:\/\/capd.ii.uj.edu.pl."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2009.23.705"},{"key":"R4","unstructured":"CHomP\u2014Computational Homology Project\n                      , Web site and software source at http:\/\/chomp.rutgers.edu."},{"key":"R5","unstructured":"M. Dellnitz and O. Junge,\n                      GAIO\u2014Global analysis of invariant objects\n                      , http:\/\/www2.math.uni-paderborn.de\/ags\/ag-dellnitz\/software.html http:\/\/www2.math.uni-paderborn.de\/ags\/ag-dellnitz\/software.html."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2004.03.014"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"J. Guckenheimer and P. Holmes,\n                      Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields\n                      , Appl. Math. Sci. 43, Springer-Verlag, New York, 1983.","DOI":"10.1007\/978-1-4612-1140-2"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01608556"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-006-0141-2"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2006.15.529"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"A. Katok and B. 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Wilczak,\n                      personal home page\n                      , http:\/\/www.ii.uj.edu.pl\/ wilczak."},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2009.11.1039"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1007\/s102080010025"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2008.12.019"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/100795176","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:16:28Z","timestamp":1787231788000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/100795176"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":27,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/100795176"],"URL":"https:\/\/doi.org\/10.1137\/100795176","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}