On two-dimensional Hamiltonian systems with sixth-order integrals of motion
E.O. Porubov, A. V. Tsiganov
TL;DR
This paper identifies 21 specific two-dimensional Hamiltonian systems that possess sixth-order polynomial invariants, expanding the understanding of integrable systems with higher-order conserved quantities.
Contribution
It provides a catalog of 21 Hamiltonian systems with sextic invariants, offering new examples for the mathematical theory of integrable systems with higher-order integrals.
Findings
Identified 21 Hamiltonian systems with sixth-order invariants
Demonstrated methods to construct systems with higher-order integrals
Contributed to the mathematical theory of integrability
Abstract
We obtain 21 two-dimensional natural Hamiltonian systems with sextic invariants, which are polynomial of the sixth order in momenta. Following to Bertrand, Darboux, and Drach these results of the standard brute force experiments can be applied to construct a new mathematical theory.
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