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In this paper, we present a generalization of the parameterization method,introduced by Cabr\'{e}, Fontich and De la Llave, to center manifoldsassociated to non-hyperbolic fixed points of discrete dynamical systems. As abyproduct, we find a new proof for the existence and regularity of centermanifolds. However, in contrast to the classical center manifold theorem, ourparameterization method will simultaneously obtain the center manifold and itsconjugate center dynamical system. Furthermore, we will provide bounds on theerror between approximations of the center manifold and the actual centermanifold, as well as bounds for the error in the conjugate dynamical system.

The parameterization method for center manifolds