Abstract
We refine the notion of generalized symmetry of a plane autonomous system of differential equations used by I.S. Kukles in the generalized symmetry method. A formula relating the Kukles and Otrokov theorems on necessary and sufficient conditions for the isochronicity of the center of the Lienard system is obtained. It is shown that the Lienard system has a generalized symmetry. A new normal form (a system with a symmetry of the direction field) is introduced for the Lienard system. A theorem on necessary and sufficient conditions for the isochronicity of the center of the Lienard system is proved. Examples of irreversible isochronous Lienard systems and methods for their construction are given.
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