In 1926 Arnaud Denjoy and Julius Wolff proved the Denjoy-Wollf Theorem (not a coincidence) which looks at the behaviour of holomorphic functions on a disc in the complex plane. Anders Karlsson and Roger Nussbaum have both conjectured that this Theorem should also hold in a more general setting, with metric spaces and non-expansive maps. This conjecture remains an open problem today, though progress has been booked in special cases. I will give a gentle introduction to this area of mathematics and will elaborate on the solutions of some of the special cases.<\/p>\n","protected":false},"excerpt":{"rendered":"