Construction of classical superintegrable systems with higher order integrals of motion from ladder operators

Understand

We construct integrals of motion for multidimensional classical systems from ladder operators of one-dimensional systems.

• This method can be used to obtain new systems with higher order integrals.
• We show how these integrals generate a polynomial Poisson algebra.
• We consider a one-dimensional system with third order ladders operators and found a family of superintegrable systems with higher order integrals of motion.