Seminar of Research Training Group
Invariant classification and limits of superintegrable systems
Tuesday July 21, 2015 16:15:00 CEST
Tuesday July 21, 2015 17:45:00 CEST
Dr. Jonathan Kress, University of New South Wales (Sydney)
A classical Hamiltonian system possessing more globally defined conserved quantities than degrees of freedom is said to be superintegrable. Such systems possessing the maximum number of conserved quantities quadratic in the momenta have been much studied because of their connection with separation of variables and special functions. In two dimensions it has been shown that singular limits between `non-degenerate' superintegrable systems mirror limits between othogonal polynomials in the Askey scheme. As a first step in extending this to higher dimensions, all second order superintegrable systems with a `non-degenerate' potential have recently been classified and shown to arise by singular limits from a generic system on the 3-sphere. This classification and the relationships between the systems, which is joint work with Joshua Capel and Sarah Post, will be discussed.
SR 5, Helmholtzweg 4