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Extensive work has been done on the group classification of systems ofequations in the literature. This paper identifies the gap in the literaturewhich concerns the group classification of systems of two autonomous nonlinearsecond-order ordinary differential equations. We provide a complete groupclassification using two approaches which form the essence of this paper andargue that this can be applied to systems of autonomous nonlinear second-orderordinary differential equations which occur in many physical applications.

Complete Group Classification of Systems of Two Nonlinear Second-Order  Ordinary Differential Equations of the Form ${\bf y}^{\prime\prime}={\bf  F}({\bf y})$