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Bifurcation Chaos"],"published-print":{"date-parts":[[2017,7]]},"abstract":"<jats:p>In this paper, the unique normal form for a class of three-dimensional nilpotent vector fields with symmetry is investigated. The key technique used is a combination of multiple Lie brackets, linear grading function, new notations of block matrices and first integral of the linear part of the given vector field which avoids complicated calculations. 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