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An analytical method for investigation of the evolution of dynamical systems{\it with independent on time accuracy} is developed for perturbed Hamiltoniansystems. The error-free estimation using of computer algebra enables theapplication of the method to complex multi-dimensional Hamiltonian anddissipative systems. It also opens principal opportunities for the qualitativestudy of chaotic trajectories. The performance of the method is demonstrated onperturbed two-oscillator systems. It can be applied to various non-linearphysical and astrophysical systems, e.g. to the long-term planetary dynamics.

Evolution of perturbed dynamical systems: analytical computation with time independent accuracy