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.
