Notes on a study of vector bundle dynamical systems (II) - Part 1

The study of linear and global properties of linear dynamical systems on vector bundles appeared rather extensive already in the past. The perturbations of the linear dynamics was studied in this paper. The perturbed dynamical system is no longer linear, and the global property was investigated in general, especially the nonuniformly hyperbolic property was concentrated. An appropriate definition for such perturbations was set at first, though it appears somewhat not quite usual, yet has deeper root in standard systems of differential equations in the theory of differential dynamical systems. The general problem is to see which property of the original is persistent when a perturbation takes place. The whole content of the paper was devoted to establishing a theorem of this sort.EI04805-818