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We apply these new algorithms to the standard map at different values of the perturbative parameter $\\varepsilon$ and obtain rigorous lower bounds for its topological entropy for $\\varepsilon\\in[.7,2]$.<\/jats:p>","DOI":"10.1137\/100808587","type":"journal-article","created":{"date-parts":[[2012,1,24]],"date-time":"2012-01-24T18:23:35Z","timestamp":1327429415000},"page":"82-109","source":"Crossref","is-referenced-by-count":4,"title":["Efficient Automation of Index Pairs in Computational Conley Index Theory"],"prefix":"10.1137","volume":"11","author":[{"given":"Rafael","family":"Frongillo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rodrigo","family":"Trevi\u00f1o","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,1,24]]},"reference":[{"key":"R1","unstructured":"Computational Homology Project (CHomP)\n                      , http:\/\/chomp.rutgers.edu."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127407017549"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/070695599"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2004.12.003"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/070688080"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/030600210"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"S. 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