Addition theorems and the Drach superintegrable systems
A. V. Tsiganov
TL;DR
This paper introduces a novel method for constructing polynomial integrals of motion using addition theorems, leading to the reconstruction of Drach systems and the discovery of new superintegrable systems with higher-order integrals.
Contribution
It presents a new approach to build polynomial integrals of motion via addition theorems, expanding the class of known superintegrable systems.
Findings
Reconstructed Drach systems using the new method
Discovered new superintegrable Stackel systems with third, fifth, and seventh order integrals
Demonstrated the effectiveness of addition theorems in integrable systems
Abstract
We propose new construction of the polynomial integrals of motion related to the addition theorems. As an example we reconstruct Drach systems and get some new two-dimensional superintegrable Stackel systems with third, fifth and seventh order integrals of motion.
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