# Superintegrable Models on Riemannian Surfaces of Revolution with Integrals of any Integer Degree (I)

*2017, Volume 22, Number 4, pp. 319-352*

Author(s):

**Valent G.**

We present a family of superintegrable (SI) systems which live on a Riemannian
surface of revolution and which exhibit one linear integral and two integrals of any integer
degree larger or equal to 2 in the momenta. When this degree is 2, one recovers a metric due
to Koenigs.
The local structure of these systems is under control of a

*linear*ordinary differential equation of order $n$ which is homogeneous for even integrals and weakly inhomogeneous for odd integrals. The form of the integrals is explicitly given in the so-called “simple” case (see Definition 2). Some globally defined examples are worked out which live either in $\mathbb{H}^2$ or in $\mathbb{R}^2$.
Access to the full text on the Springer website |