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The derivation of conservation laws and invariant functions is an essentialprocedure for the investigation of nonlinear dynamical systems. In this studywe consider a two-field cosmological model with scalar fields defined in theJordan frame. In particular we consider a Brans-Dicke scalar field theory andfor the second scalar field we consider a quintessence scalar field minimallycoupled to gravity. For this cosmological model we apply for the first time anew technique for the derivation of conservation laws without the applicationof variational symmetries. The results are applied for the derivation of newexact solutions. The stability properties of the scaling solutions areinvestigated and criteria for the nature of the second field according to thestability of these solutions are determined.

New conservation laws and exact cosmological solutions in Brans-Dicke cosmology with an extra scalar field