Stability of integral manifold and orbital attraction of quasi-periodic motion (Q685815)

The system under consideration reads \(z'=A(\theta,t,\lambda)z+F(z,\theta,t,\lambda)\), \(\theta'=Q(\theta,t,\lambda)+ G(z,\theta,t,\lambda)\), where \((z,\theta,\lambda)\in \mathbb{R}^ n\times \mathbb{T}^ k \times\mathbb{R}^ m\), \(F=0(| z|^ 2)\), \(G=0(| z|)\), as far as \(\lambda=0\). In this large paper, the main emphasis is focused on the stability investigation of the above system. The novelty consists especially in the nonclassical construction of the related stable and unstable manifolds. The obtained criteria are, nevertheless, rather sophisticated.