Superintegrable models on riemannian surfaces of revolution with integrals of any integer degree (I)

2017/03/31 by Galliano, Valent
#32C05 #37E99 #37K25 #81V99 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1703.10870

Abstract

We present a family of superintegrable (SI) sytems living on a riemannian surface of revolution and which exhibits 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 H2 or in R2.

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