The concepts of persistent and weakly persistent centers were introduced in 2009 and the same concept was applied in the study of some families of differential equations in 2013. Such concept was generalized for complex planar differential systems in 2014. In this paper we extend the notion of persistent center to a linearizable persistent center and a linearizable weakly persistent center. Using the methods and algorithms of computational algebra we characterize the planar cubic differential system having linearizable persistent and linearizable weakly persistent centers at the origin. Keywords: linearizability problem, center problem, focus quantities, persistent center. 2010 Mathematics Subject Classification: 34C25, 34M35, 37C10, 37C27.
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