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We present an explicit form of cubic systems with a nilpotent singular point of the focus or center type at the origin. A method for finding the focus quantities of such systems is indicated. Sufficient conditions for the existence of a nilpotent center for cubic systems are given. Cubic systems reducible to the Li´enard system are studied in detail.
A criterion is suggested for defining such properties of the right-hand sides in the Lienard polynomial system that guarantee its first absolute invariant turning to a constant.