Superintegrability of a resonant ghostly tri-Hamiltonian model: polynomial first integrals and transcendental completion
The study investigates superintegrability in a resonant three-dimensional Hamiltonian system with indefinite kinetic energy. It finds that while the system is minimally superintegrable using polynomial and rational first integrals, maximal superintegrability is achieved only when transcendental first integrals are included. This means the system requires non-polynomial functions to achieve its highest level of integrability.