Effective algorithm of analysis of integrability via the Ziglin's method

TL;DR

This paper presents a constructive algorithm based on Ziglin's method for analyzing the integrability of dynamical systems, emphasizing numerical simulations and algebraic techniques with successful real-world applications.

Contribution

It introduces a new, constructive algorithm derived from Ziglin's approach for computer-assisted integrability analysis of dynamical systems.

Findings

Algorithm successfully applied to physical systems

Numerical simulations enhance rigorous integrability analysis

Algebraic methods complement numerical approaches

Abstract

In this paper we continue the description of the possibilities to use numerical simulations for mathematically rigorous computer assisted analysis of integrability of dynamical systems. We sketch some of the algebraic methods of studying the integrability and present a constructive algorithm issued from the Ziglin's approach. We provide some examples of successful applications of the constructed algorithm to physical systems.