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Not much work was done in this direction to start with, but recently there have been various developments. Here, first the original work of Lie (and the early developments on it), and then more recent developments based on geometry and complex analysis, apart from Lie\u2019s own method of algebra (namely, Lie group theory), are reviewed. It is relevant to mention that much of the work is <jats:italic>not<\/jats:italic> linearization but uses the base of linearization.<\/jats:p>","DOI":"10.1155\/2012\/303960","type":"journal-article","created":{"date-parts":[[2012,12,27]],"date-time":"2012-12-27T21:01:00Z","timestamp":1356642060000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Linearization: Geometric, Complex, and Conditional"],"prefix":"10.1155","volume":"2012","author":[{"given":"Asghar","family":"Qadir","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,12,27]]},"reference":[{"key":"e_1_2_10_1_2","article-title":"Analyse d\u2019un memoire sur la rsolution algbrique des quations","volume":"13","author":"Galois E.","year":"1830","journal-title":"Bulletin des Sciences Math\u00e9matiques Journal"},{"key":"e_1_2_10_2_2","article-title":"Theorie der Transformationsgruppen","volume":"16","author":"Lie S.","year":"1880","journal-title":"Mathematische Annalen"},{"key":"e_1_2_10_3_2","article-title":"Klassifikation und integration von gew\u00f6nlichen differentialgleichungenzwischen x, y, die eine gruppe von transformationen gestaten","volume":"8","author":"Lie S.","year":"1883","journal-title":"Archiv for Matematik"},{"volume-title":"Lectures on Differential Equations with Known Infinitesimal Transformations","year":"1891","author":"Sheffers G.","key":"e_1_2_10_4_2"},{"volume-title":"Differential Equations","year":"1967","key":"e_1_2_10_5_2"},{"key":"e_1_2_10_6_2","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/BF02418270","article-title":"Sur les invariants differentiels des groupes continus de transformations","volume":"18","author":"Tresse A.","year":"1894","journal-title":"Acta Mathematica"},{"key":"e_1_2_10_7_2","first-page":"1227","article-title":"Sur la geometrie d\u2032une equation differentielle du troiseme orde","volume":"204","author":"Chern S. 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