Exponential stability of an invariant torus of a nonlinear countable system of differential equations (Q917766)

Consider the nonlinear denumerable system of differential equations (*): \(d\phi /dt=a(\phi,h)\), \(dh/dt=P(\phi,h)h+c(\phi),\) where \(\phi =(\phi_ 1,\phi_ 2,...,\phi_ m)\), \(h=(h_ 1,h_ 2,...)\), a(\(\phi\),h), c(\(\phi\)) are continuous vector functions, \(P(\phi,h)=(p_{ij}(\phi,h))^{\infty}_{i,j=1}\) is an infinite matrix function, and \(\phi\) is periodic in \(\phi_ i\) with \(2\pi\)-period. The author gives some conditions under which any trajectory starting from a small neighborhood of an invariant torus of system (*) exponentially approaches a certain trajectory on the torus.