Evolution of perturbed dynamical systems: analytical computation with   time independent accuracy
  An analytical method for investigation of the evolution of dynamical systems {\it with independent on time accuracy} is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application of the method to complex multi-dimensional Hamiltonian and dissipative systems. It also opens principal opportunities for the qualitative study of chaotic trajectories. The performance of the method is demonstrated on perturbed two-oscillator systems. It can be applied to various non-linear physical and astrophysical systems, e.g. to the long-term planetary dynamics. 
A.V. Gurzadyan, A.A. Kocharyan
astro-ph.IM astro-ph.GA physics.comp-ph