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

TL;DR

This paper introduces an analytical method for studying the evolution of perturbed dynamical systems with time-independent accuracy, leveraging computer algebra to handle complex multi-dimensional Hamiltonian and dissipative systems, including chaotic trajectories.

Contribution

The paper presents a novel analytical approach that achieves error-free evolution estimation for complex perturbed systems, enabling new qualitative analyses of chaotic dynamics.

Findings

Method successfully applied to two-oscillator systems

Allows long-term analysis of planetary dynamics

Enables qualitative study of chaotic trajectories

Abstract

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.